Multiples of 18

Multiples of 18 are numbers that result from multiplying 18 by any integer. In mathematics, a multiple is the product of a given number and an integer. The concept of multiples is closely related to the ideas of factors and divisors, where factors of 18 are numbers that divide 18 exactly without leaving a remainder. Understanding multiples of 18 helps in various arithmetic operations, including finding common multiples and solving problems involving division and multiplication. These multiples are integral in number theory and have applications in many areas of mathematics.

What are Multiples of 18?

Multiples of 18 are the numbers you get when you multiply 18 by any integer. Examples include 18, 36, 54, 72, and so on. These multiples are essential in understanding arithmetic operations involving division and multiplication.

Prime Factorization of 18: 18 = 2 × 3² First 10 multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180.

For example, 54, 90, 144 and 162 are all multiples of 18, 170 is not a multiple of 18 for the following reasons:

Number	Reason	Remainder
54	54 is a multiple of 18 because 18×3 = 54.	0
90	90 is a multiple of 18 because 18×5 = 90.	0
144	144 is a multiple of 18 because 18×8 = 144.	0
162	162 is a multiple of 18 because 18×9 = 162.	0
170	170 is not a multiple of 18 because 170÷18 does not result in an integer.	8

List of First 100 Multiples of 18 with Remainders

Multiple	Reason	Remainder
18	18 is a multiple of 18 because 18×1 = 18.	0
36	36 is a multiple of 18 because 18×2 = 36.	0
54	54 is a multiple of 18 because 18×3 = 54.	0
72	72 is a multiple of 18 because 18×4 = 72.	0
90	90 is a multiple of 18 because 18×5 = 90.	0
108	108 is a multiple of 18 because 18×6 = 108.	0
126	126 is a multiple of 18 because 18×7 = 126.	0
144	144 is a multiple of 18 because 18×8 = 144.	0
162	162 is a multiple of 18 because 18×9 = 162.	0
180	180 is a multiple of 18 because 18×10 = 180.	0
198	198 is a multiple of 18 because 18×11 = 198.	0
216	216 is a multiple of 18 because 18×12 = 216.	0
234	234 is a multiple of 18 because 18×13 = 234.	0
252	252 is a multiple of 18 because 18×14 = 252.	0
270	270 is a multiple of 18 because 18×15 = 270.	0
288	288 is a multiple of 18 because 18×16 = 288.	0
306	306 is a multiple of 18 because 18×17 = 306.	0
324	324 is a multiple of 18 because 18×18 = 324.	0
342	342 is a multiple of 18 because 18×19 = 342.	0
360	360 is a multiple of 18 because 18×20 = 360.	0
378	378 is a multiple of 18 because 18×21 = 378.	0
396	396 is a multiple of 18 because 18×22 = 396.	0
414	414 is a multiple of 18 because 18×23 = 414.	0
432	432 is a multiple of 18 because 18×24 = 432.	0
450	450 is a multiple of 18 because 18×25 = 450.	0
468	468 is a multiple of 18 because 18×26 = 468.	0
486	486 is a multiple of 18 because 18×27 = 486.	0
504	504 is a multiple of 18 because 18×28 = 504.	0
522	522 is a multiple of 18 because 18×29 = 522.	0
540	540 is a multiple of 18 because 18×30 = 540.	0
558	558 is a multiple of 18 because 18×31 = 558.	0
576	576 is a multiple of 18 because 18×32 = 576.	0
594	594 is a multiple of 18 because 18×33 = 594.	0
612	612 is a multiple of 18 because 18×34 = 612.	0
630	630 is a multiple of 18 because 18×35 = 630.	0
648	648 is a multiple of 18 because 18×36 = 648.	0
666	666 is a multiple of 18 because 18×37 = 666.	0
684	684 is a multiple of 18 because 18×38 = 684.	0
702	702 is a multiple of 18 because 18×39 = 702.	0
720	720 is a multiple of 18 because 18×40 = 720.	0
738	738 is a multiple of 18 because 18×41 = 738.	0
756	756 is a multiple of 18 because 18×42 = 756.	0
774	774 is a multiple of 18 because 18×43 = 774.	0
792	792 is a multiple of 18 because 18×44 = 792.	0
810	810 is a multiple of 18 because 18×45 = 810.	0
828	828 is a multiple of 18 because 18×46 = 828.	0
846	846 is a multiple of 18 because 18×47 = 846.	0
864	864 is a multiple of 18 because 18×48 = 864.	0
882	882 is a multiple of 18 because 18×49 = 882.	0
900	900 is a multiple of 18 because 18×50 = 900.	0
918	918 is a multiple of 18 because 18×51 = 918.	0
936	936 is a multiple of 18 because 18×52 = 936.	0
954	954 is a multiple of 18 because 18×53 = 954.	0
972	972 is a multiple of 18 because 18×54 = 97.	0
990	990 is a multiple of 18 because 18×55 = 990.	0
1008	1008 is a multiple of 18 because 18×56 = 1008.	0
1026	1026 is a multiple of 18 because 18×57 = 1026.	0
1044	1044 is a multiple of 18 because 18×58 = 1044.	0
1062	1062 is a multiple of 18 because 18×59 = 1062.	0
1080	1080 is a multiple of 18 because 18×60 = 1080.	0
1098	1098 is a multiple of 18 because 18×61 = 1098.	0
1116	1116 is a multiple of 18 because 18×62 = 1116.	0
1134	1134 is a multiple of 18 because 18×63 = 1134.	0
1152	1152 is a multiple of 18 because 18×64 = 1152.	0
1170	1170 is a multiple of 18 because 18×65 = 1170.	0
1188	1188 is a multiple of 18 because 18×66 = 1188.	0
1206	1206 is a multiple of 18 because 18×67 = 1206.	0
1224	1224 is a multiple of 18 because 18×68 = 1224.	0
1242	1242 is a multiple of 18 because 18×69 = 1242.	0
1260	1260 is a multiple of 18 because 18×70 = 1260.	0
1278	1278 is a multiple of 18 because 18×71 = 1278.	0
1296	1296 is a multiple of 18 because 18×72 = 1296.	0
1314	1314 is a multiple of 18 because 18×73 = 1314.	0
1332	1332 is a multiple of 18 because 18×74 = 1332.	0
1350	1350 is a multiple of 18 because 18×75 = 1350.	0
1368	1368 is a multiple of 18 because 18×76 = 1368.	0
1386	1386 is a multiple of 18 because 18×77 = 1386.	0
1404	1404 is a multiple of 18 because 18×78 = 1404.	0
1422	1422 is a multiple of 18 because 18×79 = 1422.	0
1440	1440 is a multiple of 18 because 18×80 = 1440.	0
1458	1458 is a multiple of 18 because 18×81 = 1458.	0
1476	1476 is a multiple of 18 because 18×82 = 1476.	0
1494	1494 is a multiple of 18 because 18×83 = 1494.	0
1512	1512 is a multiple of 18 because 18×84 = 1512.	0
1530	1530 is a multiple of 18 because 18×85 = 1530.	0
1548	1548 is a multiple of 18 because 18×86 = 1548.	0
1566	1566 is a multiple of 18 because 18×87 = 1566.	0
1584	1584 is a multiple of 18 because 18×88 = 1584.	0
1602	1602 is a multiple of 18 because 18×89 = 1602.	0
1620	1620 is a multiple of 18 because 18×90 = 1620.	0
1638	1638 is a multiple of 18 because 18×91 = 1638.	0
1656	1656 is a multiple of 18 because 18×92 = 1656.	0
1674	1674 is a multiple of 18 because 18×93 = 1674.	0
1692	1692 is a multiple of 18 because 18×94 = 1692.	0
1710	1710 is a multiple of 18 because 18×95 = 1710.	0
1728	1728 is a multiple of 18 because 18×96 = 1728.	0
1746	1746 is a multiple of 18 because 18×97 = 1746.	0
1764	1764 is a multiple of 18 because 18×98 = 1764.	0
1782	1782 is a multiple of 18 because 18×99 = 1782.	0
1800	1800 is a multiple of 18 because 18×100 = 1800.	0

Read More About Multiples of 18

Table of 18

Important Notes

Definition: Multiples of 18 are the numbers that you get when you multiply 18 by any integer. These numbers are part of the arithmetic sequence where each term is 18 units apart.

Examples: Some common multiples of 18 include 18, 36, 54, 72, 90, and so on. Each of these is the result of 18×n, where n is an integer.

Identification: To determine if a number is a multiple of 18, divide the number by 18. If the result is an integer without any remainder, then the number is a multiple of 18.

Relationship to Factors: Factors of 18 (1, 2, 3, 6, 9, 18) are numbers that divide 18 exactly. Multiples of 18, on the other hand, are numbers that 18 divides exactly.

Applications: Multiples of 18 are useful in solving problems related to common multiples, least common multiples (LCM), and in various arithmetic operations involving division and multiplication.

Pattern: Multiples of 18 follow a consistent pattern in arithmetic sequences. They can be generated by repeatedly adding 18 to the previous multiple.

Divisibility: A number is divisible by 18 if it is divisible by both 2 and 9. This is because 18 is the product of these two prime factors (2×9 = 18).

Examples on Multiples of 18

First 10 Multiples of 18:

• 18, 36, 54, 72, 90, 108, 126, 144, 162, 180

Detailed Examples:

• 18×1 = 18
• 18×2 = 36
• 18×3 = 54
• 18×4 = 72
• 18×5 = 90
• 18×6 = 108
• 18×7 = 126
• 18×8 = 144
• 18×9 = 162
• 18×10 = 180

Real-World Example:

• If you have 18 apples and you want to distribute them equally among different groups, any group size that is a multiple of 18 (e.g., 36, 54) will work perfectly without leaving any apples behind.

Checking for Multiples:

Example 1: Is 54 a multiple of 18?

• Calculation: 54÷18 = 3
• Result: Yes, because the quotient is an integer.

Example 2: Is 100 a multiple of 18?

• Calculation: 100÷18 = 5.555…
• Result: No, because the quotient is not an integer.

Common Multiples:

Example: Find the least common multiple (LCM) of 18 and 24.

• Multiples of 18: 18, 36, 54, 72, 90, 108, …
• Multiples of 24: 24, 48, 72, 96, 120, …
• LCM: 72

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