LCM for 4, 16 and 20

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

What's the Least Common Multiple (LCM) of 4, 16 and 20?

Answer

LCM of 4, 16 and 20 is
80

(Eighty)

80 is the smallest positive integer that 4, 16 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 16 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 4: 2 × 2 (exponent form: 22)

All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

Prime factor41620Highest power
222242224
5——55

LCM = 24 × 5 = 80

Checking the LCM of 4, 16 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(4, 16) = (4 × 16) ÷ 4 = 64 ÷ 4 = 16

LCM(16, 20) = (16 × 20) ÷ 4 = 320 ÷ 4 = 80

LCM(4, 16, 20) = 80

The pairs may be taken in any order — 16 and 20 first, then 4 — and the answer is the same 80. 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, 16 and 20? (The answer is: 80). Enter the first number (e.g. '4'), the second (e.g. '16') 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
451680
461648
4716112
481616
4916144
4101680
41116176
4121648
41316208
41416112
41516240
4161616
41617272
41618144
41619304
4162080
41621336
41622176
41623368
4162448
41625400
41626208
41627432
41628112
41629464
41630240
41631496
4163232
41633528
41634272

FAQ

What's the Least Common Multiple (LCM) of 4, 16 and 20?

LCM of 4, 16 and 20 is 80

How to find the LCM of 4, 16 and 20 by prime factorization?

Take every prime that appears in 4, 16 and 20 to the highest power it reaches in any one of them and multiply: 2⁴ × 5 = 80.

Can you get the LCM of 4, 16 and 20 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 16 is 16, and the LCM of 16 and 20 is 80 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 80 divisible by 4, 16 and 20?

Yes, and by definition it is the smallest positive integer that is: 80 ÷ 4, 80 ÷ 16 and 80 ÷ 20 all come out whole. Any other common multiple of 4, 16 and 20 is a multiple of 80.

See Also