LCM for 4, 8 and 40

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

What's the Least Common Multiple (LCM) of 4, 8 and 40?

Answer

LCM of 4, 8 and 40 is
40

(Forty)

40 is the smallest positive integer that 4, 8 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 8 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 4: 2 × 2 (exponent form: 22)

All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

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

Prime factor4840Highest power
222232323
5——55

LCM = 23 × 5 = 40

Checking the LCM of 4, 8 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(4, 8) = (4 × 8) ÷ 4 = 32 ÷ 4 = 8

LCM(8, 40) = (8 × 40) ÷ 8 = 320 ÷ 8 = 40

LCM(4, 8, 40) = 40

The pairs may be taken in any order — 8 and 40 first, then 4 — and the answer is the same 40. 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 4, 8 and 40? (The answer is: 40). Enter the first number (e.g. '4'), the second (e.g. '8') 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
4825200
4826104
4827216
482856
4829232
4830120
4831248
483232
4833264
4834136
4835280
483672
4837296
4838152
4839312
484040
4841328
4842168
4843344
484488
4845360
4846184
4847376
484848
4849392
4850200
4851408
4852104
4853424
4854216

FAQ

What's the Least Common Multiple (LCM) of 4, 8 and 40?

LCM of 4, 8 and 40 is 40

How to find the LCM of 4, 8 and 40 by prime factorization?

Take every prime that appears in 4, 8 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 5 = 40.

Can you get the LCM of 4, 8 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 8 is 8, and the LCM of 8 and 40 is 40 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 40 divisible by 4, 8 and 40?

Yes, and by definition it is the smallest positive integer that is: 40 ÷ 4, 40 ÷ 8 and 40 ÷ 40 all come out whole. Any other common multiple of 4, 8 and 40 is a multiple of 40.

See Also