LCM for 7, 12 and 16

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

What's the Least Common Multiple (LCM) of 7, 12 and 16?

Answer

LCM of 7, 12 and 16 is
336

(Three hundred thirty-six)

336 is the smallest positive integer that 7, 12 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 7, 12 and 16 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 7: 7 (exponent form: 7)

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

Prime factor71216Highest power
2—222424
3—3—3
77——7

LCM = 24 × 3 × 7 = 336

Checking the LCM of 7, 12 and 16 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(7, 12) = (7 × 12) ÷ 1 = 84 ÷ 1 = 84

LCM(84, 16) = (84 × 16) ÷ 4 = 1,344 ÷ 4 = 336

LCM(7, 12, 16) = 336

The pairs may be taken in any order — 12 and 16 first, then 7 — and the answer is the same 336. That is exactly why the two routes on this page agree.

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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 7, 12 and 16? (The answer is: 336). Enter the first number (e.g. '7'), the second (e.g. '12') and the third (e.g. '16'), 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
171284
271284
371284
471284
5712420
671284
771284
7812168
7912252
71012420
71112924
7121284
712131,092
7121484
71215420
71216336
712171,428
71218252
712191,596
71220420
7122184
71222924
712231,932
71224168
712252,100
712261,092
71227756
7122884
712292,436
71230420

FAQ

What's the Least Common Multiple (LCM) of 7, 12 and 16?

LCM of 7, 12 and 16 is 336

How to find the LCM of 7, 12 and 16 by prime factorization?

Take every prime that appears in 7, 12 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

Can you get the LCM of 7, 12 and 16 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 7 and 12 is 84, and the LCM of 84 and 16 is 336 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 336 divisible by 7, 12 and 16?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 7, 336 ÷ 12 and 336 ÷ 16 all come out whole. Any other common multiple of 7, 12 and 16 is a multiple of 336.

See Also