LCM for 16, 20 and 25

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

What's the Least Common Multiple (LCM) of 16, 20 and 25?

Answer

LCM of 16, 20 and 25 is
400

(Four hundred)

400 is the smallest positive integer that 16, 20 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 20 and 25 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 25: 5 × 5 (exponent form: 52)

Prime factor162025Highest power
22422—24
5—55252

LCM = 24 × 52 = 400

Checking the LCM of 16, 20 and 25 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, 20) = (16 × 20) ÷ 4 = 320 ÷ 4 = 80

LCM(80, 25) = (80 × 25) ÷ 5 = 2,000 ÷ 5 = 400

LCM(16, 20, 25) = 400

The pairs may be taken in any order — 20 and 25 first, then 16 — and the answer is the same 400. 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, 20 and 25? (The answer is: 400). Enter the first number (e.g. '16'), the second (e.g. '20') and the third (e.g. '25'), 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
10162080
111620880
121620240
1316201,040
141620560
151620240
16162080
1617201,360
161820720
1619201,520
16202080
1620211,680
162022880
1620231,840
162024240
162025400
1620261,040
1620272,160
162028560
1620292,320
162030240
1620312,480
162032160
1620332,640
1620341,360
162035560
162036720
1620372,960
1620381,520
1620393,120

FAQ

What's the Least Common Multiple (LCM) of 16, 20 and 25?

LCM of 16, 20 and 25 is 400

How to find the LCM of 16, 20 and 25 by prime factorization?

Take every prime that appears in 16, 20 and 25 to the highest power it reaches in any one of them and multiply: 2⁴ × 5² = 400.

Can you get the LCM of 16, 20 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 20 is 80, and the LCM of 80 and 25 is 400 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 400 divisible by 16, 20 and 25?

Yes, and by definition it is the smallest positive integer that is: 400 ÷ 16, 400 ÷ 20 and 400 ÷ 25 all come out whole. Any other common multiple of 16, 20 and 25 is a multiple of 400.

See Also