LCM for 3, 7 and 20

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

What's the Least Common Multiple (LCM) of 3, 7 and 20?

Answer

LCM of 3, 7 and 20 is
420

(Four hundred twenty)

420 is the smallest positive integer that 3, 7 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 7 and 20 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 3: 3 (exponent form: 3)

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

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

Prime factor3720Highest power
2——2222
33——3
5——55
7—7—7

LCM = 22 × 3 × 5 × 7 = 420

Checking the LCM of 3, 7 and 20 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(3, 7) = (3 × 7) ÷ 1 = 21 ÷ 1 = 21

LCM(21, 20) = (21 × 20) ÷ 1 = 420 ÷ 1 = 420

LCM(3, 7, 20) = 420

The pairs may be taken in any order — 7 and 20 first, then 3 — and the answer is the same 420. 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 3, 7 and 20? (The answer is: 420). Enter the first number (e.g. '3'), the second (e.g. '7') and the third (e.g. '20'), 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
357105
36742
37721
378168
37963
3710210
3711231
371284
3713273
371442
3715105
3716336
3717357
3718126
3719399
3720420
372121
3722462
3723483
3724168
3725525
3726546
3727189
372884
3729609
3730210
3731651
3732672
3733231
3734714

FAQ

What's the Least Common Multiple (LCM) of 3, 7 and 20?

LCM of 3, 7 and 20 is 420

How to find the LCM of 3, 7 and 20 by prime factorization?

Take every prime that appears in 3, 7 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 3, 7 and 20 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 7 is 21, and the LCM of 21 and 20 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 3, 7 and 20?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 3, 420 ÷ 7 and 420 ÷ 20 all come out whole. Any other common multiple of 3, 7 and 20 is a multiple of 420.

See Also