LCM for 5, 7 and 21

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What's the Least Common Multiple (LCM) of 5, 7 and 21?

Answer

LCM of 5, 7 and 21 is
105

First common multiples: 105, 210, 315, …

105 is divisible by all three: 105 ÷ 5 = 21, 105 ÷ 7 = 15, 105 ÷ 21 = 5 — and 21, 15 and 5 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/5 by 21 and of y/7 by 15 and of z/21 by 5.

5 — prime

7 — prime

21 = 3 × 7

Prime5721Highest power
3——33
55——5
7—777

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

LCM = 3 × 5 × 7 = 105

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LCM Table

1st2nd3rdLCM
567210
57735
578280
579315
571070
5711385
5712420
5713455
571470
5715105
5716560
5717595
5718630
5719665
5720140
5721105
5722770
5723805
5724840
5725175
5726910
5727945
5728140
57291,015
5730210
57311,085
57321,120
57331,155
57341,190
573535

FAQ

What's the Least Common Multiple (LCM) of 5, 7 and 21?

LCM of 5, 7 and 21 is 105

How to find the LCM of 5, 7 and 21 by prime factorization?

Take every prime that appears in 5, 7 and 21 to the highest power it reaches in any one of them and multiply: 3 × 5 × 7 = 105.

Can you get the LCM of 5, 7 and 21 two numbers at a time?

Yes. The LCM of 5 and 7 is 35, and the LCM of 35 and 21 is 105 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 105 divisible by 5, 7 and 21?

Yes, and by definition it is the smallest positive integer that is: 105 ÷ 5, 105 ÷ 7 and 105 ÷ 21 all come out whole. Any other common multiple of 5, 7 and 21 is a multiple of 105.

See Also