LCM for 6, 21 and 45

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

What's the Least Common Multiple (LCM) of 6, 21 and 45?

Answer

LCM of 6, 21 and 45 is
630

(Six hundred thirty)

630 is the smallest positive integer that 6, 21 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 21 and 45 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 21: 3 × 7 (exponent form: 3 × 7)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor62145Highest power
22——2
3333232
5——55
7—7—7

LCM = 2 × 32 × 5 × 7 = 630

Checking the LCM of 6, 21 and 45 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, 21) = (6 × 21) ÷ 3 = 126 ÷ 3 = 42

LCM(42, 45) = (42 × 45) ÷ 3 = 1,890 ÷ 3 = 630

LCM(6, 21, 45) = 630

The pairs may be taken in any order — 21 and 45 first, then 6 — and the answer is the same 630. 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, 21 and 45? (The answer is: 630). Enter the first number (e.g. '6'), the second (e.g. '21') and the third (e.g. '45'), 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
62130210
621311,302
62132672
62133462
62134714
62135210
62136252
621371,554
62138798
62139546
62140840
621411,722
6214242
621431,806
62144924
62145630
62146966
621471,974
62148336
62149294
621501,050
62151714
621521,092
621532,226
62154378
621552,310
62156168
62157798
621581,218
621592,478

FAQ

What's the Least Common Multiple (LCM) of 6, 21 and 45?

LCM of 6, 21 and 45 is 630

How to find the LCM of 6, 21 and 45 by prime factorization?

Take every prime that appears in 6, 21 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 7 = 630.

Can you get the LCM of 6, 21 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 21 is 42, and the LCM of 42 and 45 is 630 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 630 divisible by 6, 21 and 45?

Yes, and by definition it is the smallest positive integer that is: 630 ÷ 6, 630 ÷ 21 and 630 ÷ 45 all come out whole. Any other common multiple of 6, 21 and 45 is a multiple of 630.

See Also