LCM for 10, 14 and 15

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

What's the Least Common Multiple (LCM) of 10, 14 and 15?

Answer

LCM of 10, 14 and 15 is
210

(Two hundred ten)

210 is the smallest positive integer that 10, 14 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 14 and 15 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 15: 3 × 5 (exponent form: 3 × 5)

Prime factor101415Highest power
222—2
3——33
55—55
7—7—7

LCM = 2 × 3 × 5 × 7 = 210

Checking the LCM of 10, 14 and 15 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, 15) = (70 × 15) ÷ 5 = 1,050 ÷ 5 = 210

LCM(10, 14, 15) = 210

The pairs may be taken in any order — 14 and 15 first, then 10 — and the answer is the same 210. 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 15? (The answer is: 210). Enter the first number (e.g. '10'), the second (e.g. '14') and the third (e.g. '15'), 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
1101470
2101470
31014210
41014140
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

FAQ

What's the Least Common Multiple (LCM) of 10, 14 and 15?

LCM of 10, 14 and 15 is 210

How to find the LCM of 10, 14 and 15 by prime factorization?

Take every prime that appears in 10, 14 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

Can you get the LCM of 10, 14 and 15 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 15 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 210 divisible by 10, 14 and 15?

Yes, and by definition it is the smallest positive integer that is: 210 ÷ 10, 210 ÷ 14 and 210 ÷ 15 all come out whole. Any other common multiple of 10, 14 and 15 is a multiple of 210.

See Also