LCM for 17, 23 and 29

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

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

Answer

LCM of 17, 23 and 29 is
11,339

(Eleven thousand three hundred thirty-nine)

11,339 is the smallest positive integer that 17, 23 and 29 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 17, 23 and 29 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 17: 17 (exponent form: 17)

All Prime Factors of 23: 23 (exponent form: 23)

All Prime Factors of 29: 29 (exponent form: 29)

Prime factor172329Highest power
1717——17
23—23—23
29——2929

LCM = 17 × 23 × 29 = 11,339

Checking the LCM of 17, 23 and 29 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(17, 23) = (17 × 23) ÷ 1 = 391 ÷ 1 = 391

LCM(391, 29) = (391 × 29) ÷ 1 = 11,339 ÷ 1 = 11,339

LCM(17, 23, 29) = 11,339

The pairs may be taken in any order — 23 and 29 first, then 17 — and the answer is the same 11,339. That is exactly why the two routes on this page agree.

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 17, 23 and 29? (The answer is: 11,339). Enter the first number (e.g. '17'), the second (e.g. '23') and the third (e.g. '29'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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