LCM for 18, 30 and 42

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What's the Least Common Multiple (LCM) of 18, 30 and 42?

Answer

LCM of 18, 30 and 42 is
630

First common multiples: 630; 1,260; 1,890; …

630 is divisible by all three: 630 ÷ 18 = 35, 630 ÷ 30 = 21, 630 ÷ 42 = 15 — and 35, 21 and 15 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/18 by 35 and of y/30 by 21 and of z/42 by 15.

18 = 2 × 32

30 = 2 × 3 × 5

42 = 2 × 3 × 7

Prime183042Highest power
22222
3323332
5—5—5
7——77

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 32 × 5 × 7 = 630

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LCM Table

1st2nd3rdLCM
182730270
1828301,260
1829302,610
18303090
1830312,790
1830321,440
183033990
1830341,530
183035630
183036180
1830373,330
1830381,710
1830391,170
183040360
1830413,690
183042630
1830433,870
1830441,980
18304590
1830462,070
1830474,230
183048720
1830494,410
183050450
1830511,530
1830522,340
1830534,770
183054270
183055990
1830562,520

FAQ

What's the Least Common Multiple (LCM) of 18, 30 and 42?

LCM of 18, 30 and 42 is 630

How to find the LCM of 18, 30 and 42 by prime factorization?

Take every prime that appears in 18, 30 and 42 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 7 = 630.

Can you get the LCM of 18, 30 and 42 two numbers at a time?

Yes. The LCM of 18 and 30 is 90, and the LCM of 90 and 42 is 630 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 630 divisible by 18, 30 and 42?

Yes, and by definition it is the smallest positive integer that is: 630 ÷ 18, 630 ÷ 30 and 630 ÷ 42 all come out whole. Any other common multiple of 18, 30 and 42 is a multiple of 630.

See Also