LCM for 28, 42 and 105

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What's the Least Common Multiple (LCM) of 28, 42 and 105?

Answer

LCM of 28, 42 and 105 is
420

First common multiples: 420; 840; 1,260; …

420 is divisible by all three: 420 ÷ 28 = 15, 420 ÷ 42 = 10, 420 ÷ 105 = 4 — and 15, 10 and 4 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/28 by 15 and of y/42 by 10 and of z/105 by 4.

28 = 22 × 7

42 = 2 × 3 × 7

105 = 3 × 5 × 7

Prime2842105Highest power
2222—22
3—333
5——55
77777

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

LCM = 22 × 3 × 5 × 7 = 420

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LCM Table

1st2nd3rdLCM
2842901,260
2842911,092
2842921,932
2842932,604
2842943,948
2842957,980
284296672
2842978,148
284298588
2842992,772
28421002,100
28421018,484
28421021,428
28421038,652
28421042,184
2842105420
28421064,452
28421078,988
2842108756
28421099,156
28421104,620
28421113,108
2842112336
28421139,492
28421141,596
28421159,660
28421162,436
28421173,276
28421184,956
28421191,428

FAQ

What's the Least Common Multiple (LCM) of 28, 42 and 105?

LCM of 28, 42 and 105 is 420

How to find the LCM of 28, 42 and 105 by prime factorization?

Take every prime that appears in 28, 42 and 105 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 28, 42 and 105 two numbers at a time?

Yes. The LCM of 28 and 42 is 84, and the LCM of 84 and 105 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 28, 42 and 105?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 28, 420 ÷ 42 and 420 ÷ 105 all come out whole. Any other common multiple of 28, 42 and 105 is a multiple of 420.

See Also