LCM for 6, 7 and 9

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

What's the Least Common Multiple (LCM) of 6, 7 and 9?

Answer

LCM of 6, 7 and 9 is
126

(One hundred twenty-six)

126 is the smallest positive integer that 6, 7 and 9 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 7 and 9 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 6: 2 × 3 (exponent form: 2 × 3)

All Prime Factors of 7: 7 (exponent form: 7)

All Prime Factors of 9: 3 × 3 (exponent form: 32)

Prime factor679Highest power
22——2
33—3232
7—7—7

LCM = 2 × 32 × 7 = 126

Checking the LCM of 6, 7 and 9 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(6, 7) = (6 × 7) ÷ 1 = 42 ÷ 1 = 42

LCM(42, 9) = (42 × 9) ÷ 3 = 378 ÷ 3 = 126

LCM(6, 7, 9) = 126

The pairs may be taken in any order — 7 and 9 first, then 6 — and the answer is the same 126. 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 6, 7 and 9? (The answer is: 126). Enter the first number (e.g. '6'), the second (e.g. '7') and the third (e.g. '9'), 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
16742
26742
36742
46784
567210
66742
67742
678168
679126
6710210
6711462
671284
6713546
671442
6715210
6716336
6717714
6718126
6719798
6720420
672142
6722462
6723966
6724168
67251,050
6726546
6727378
672884
67291,218
6730210

FAQ

What's the Least Common Multiple (LCM) of 6, 7 and 9?

LCM of 6, 7 and 9 is 126

How to find the LCM of 6, 7 and 9 by prime factorization?

Take every prime that appears in 6, 7 and 9 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

Can you get the LCM of 6, 7 and 9 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 7 is 42, and the LCM of 42 and 9 is 126 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 126 divisible by 6, 7 and 9?

Yes, and by definition it is the smallest positive integer that is: 126 ÷ 6, 126 ÷ 7 and 126 ÷ 9 all come out whole. Any other common multiple of 6, 7 and 9 is a multiple of 126.

See Also