LCM for 10, 12 and 40

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

What's the Least Common Multiple (LCM) of 10, 12 and 40?

Answer

LCM of 10, 12 and 40 is
120

(One hundred twenty)

120 is the smallest positive integer that 10, 12 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 12 and 40 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor101240Highest power
22222323
3—3—3
55—55

LCM = 23 × 3 × 5 = 120

Checking the LCM of 10, 12 and 40 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, 12) = (10 × 12) ÷ 2 = 120 ÷ 2 = 60

LCM(60, 40) = (60 × 40) ÷ 20 = 2,400 ÷ 20 = 120

LCM(10, 12, 40) = 120

The pairs may be taken in any order — 12 and 40 first, then 10 — and the answer is the same 120. That is exactly why the two routes on this page agree.

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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 10, 12 and 40? (The answer is: 120). Enter the first number (e.g. '10'), the second (e.g. '12') and the third (e.g. '40'), 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
101225300
101226780
101227540
101228420
1012291,740
10123060
1012311,860
101232480
101233660
1012341,020
101235420
101236180
1012372,220
1012381,140
101239780
101240120
1012412,460
101242420
1012432,580
101244660
101245180
1012461,380
1012472,820
101248240
1012492,940
101250300
1012511,020
101252780
1012533,180
101254540

FAQ

What's the Least Common Multiple (LCM) of 10, 12 and 40?

LCM of 10, 12 and 40 is 120

How to find the LCM of 10, 12 and 40 by prime factorization?

Take every prime that appears in 10, 12 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 10, 12 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 12 is 60, and the LCM of 60 and 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 10, 12 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 12 and 120 ÷ 40 all come out whole. Any other common multiple of 10, 12 and 40 is a multiple of 120.

See Also