LCM for 16, 24 and 40

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

What's the Least Common Multiple (LCM) of 16, 24 and 40?

Answer

LCM of 16, 24 and 40 is
240

(Two hundred forty)

240 is the smallest positive integer that 16, 24 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 24 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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

Prime factor162440Highest power
224232324
3—3—3
5——55

LCM = 24 × 3 × 5 = 240

Checking the LCM of 16, 24 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(16, 24) = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

LCM(48, 40) = (48 × 40) ÷ 8 = 1,920 ÷ 8 = 240

LCM(16, 24, 40) = 240

The pairs may be taken in any order — 24 and 40 first, then 16 — and the answer is the same 240. 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 16, 24 and 40? (The answer is: 240). Enter the first number (e.g. '16'), the second (e.g. '24') 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
1624251,200
162426624
162427432
162428336
1624291,392
162430240
1624311,488
16243296
162433528
162434816
1624351,680
162436144
1624371,776
162438912
162439624
162440240
1624411,968
162442336
1624432,064
162444528
162445720
1624461,104
1624472,256
16244848
1624492,352
1624501,200
162451816
162452624
1624532,544
162454432

FAQ

What's the Least Common Multiple (LCM) of 16, 24 and 40?

LCM of 16, 24 and 40 is 240

How to find the LCM of 16, 24 and 40 by prime factorization?

Take every prime that appears in 16, 24 and 40 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

Can you get the LCM of 16, 24 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 24 is 48, and the LCM of 48 and 40 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 240 divisible by 16, 24 and 40?

Yes, and by definition it is the smallest positive integer that is: 240 ÷ 16, 240 ÷ 24 and 240 ÷ 40 all come out whole. Any other common multiple of 16, 24 and 40 is a multiple of 240.

See Also