LCM for 17, 23 and 29

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What's the Least Common Multiple (LCM) of 17, 23 and 29?

Answer

LCM of 17, 23 and 29 is
11,339

First common multiples: 11,339; 22,678; 34,017; …

11,339 is divisible by all three: 11,339 ÷ 17 = 667; 11,339 ÷ 23 = 493; 11,339 ÷ 29 = 391 — and 667, 493 and 391 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/17 by 667 and of y/23 by 493 and of z/29 by 391.

17 — prime

23 — prime

29 — prime

Prime172329Highest power
1717——17
23—23—23
29——2929

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

LCM = 17 × 23 × 29 = 11,339

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LCM Table

1st2nd3rdLCM
1417235,474
1517235,865
1617236,256
171723391
1718237,038
1719237,429
1720237,820
1721238,211
1722238,602
172323391
1723249,384
1723259,775
17232610,166
17232710,557
17232810,948
17232911,339
17233011,730
17233112,121
17233212,512
17233312,903
172334782
17233513,685
17233614,076
17233714,467
17233814,858
17233915,249
17234015,640
17234116,031
17234216,422
17234316,813

FAQ

What's the Least Common Multiple (LCM) of 17, 23 and 29?

LCM of 17, 23 and 29 is 11,339

How to find the LCM of 17, 23 and 29 by prime factorization?

Take every prime that appears in 17, 23 and 29 to the highest power it reaches in any one of them and multiply: 17 × 23 × 29 = 11,339.

Can you get the LCM of 17, 23 and 29 two numbers at a time?

Yes. The LCM of 17 and 23 is 391, and the LCM of 391 and 29 is 11,339 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 11,339 divisible by 17, 23 and 29?

Yes, and by definition it is the smallest positive integer that is: 11,339 ÷ 17, 11,339 ÷ 23 and 11,339 ÷ 29 all come out whole. Any other common multiple of 17, 23 and 29 is a multiple of 11,339.

See Also