LCM for 10, 14 and 20

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

What's the Least Common Multiple (LCM) of 10, 14 and 20?

Answer

LCM of 10, 14 and 20 is
140

(One hundred forty)

140 is the smallest positive integer that 10, 14 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 14 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 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

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

Prime factor101420Highest power
2222222
55—55
7—7—7

LCM = 22 × 5 × 7 = 140

Checking the LCM of 10, 14 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(10, 14) = (10 × 14) ÷ 2 = 140 ÷ 2 = 70

LCM(70, 20) = (70 × 20) ÷ 10 = 1,400 ÷ 10 = 140

LCM(10, 14, 20) = 140

The pairs may be taken in any order — 14 and 20 first, then 10 — and the answer is the same 140. 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 10, 14 and 20? (The answer is: 140). Enter the first number (e.g. '10'), the second (e.g. '14') 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
5101470
61014210
7101470
81014280
91014630
10101470
101114770
101214420
101314910
10141470
101415210
101416560
1014171,190
101418630
1014191,330
101420140
101421210
101422770
1014231,610
101424840
101425350
101426910
1014271,890
101428140
1014292,030
101430210
1014312,170
1014321,120
1014332,310
1014341,190

FAQ

What's the Least Common Multiple (LCM) of 10, 14 and 20?

LCM of 10, 14 and 20 is 140

How to find the LCM of 10, 14 and 20 by prime factorization?

Take every prime that appears in 10, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

Can you get the LCM of 10, 14 and 20 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 14 is 70, and the LCM of 70 and 20 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 140 divisible by 10, 14 and 20?

Yes, and by definition it is the smallest positive integer that is: 140 ÷ 10, 140 ÷ 14 and 140 ÷ 20 all come out whole. Any other common multiple of 10, 14 and 20 is a multiple of 140.

See Also