LCM for 15, 25 and 100

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

What's the Least Common Multiple (LCM) of 15, 25 and 100?

Answer

LCM of 15, 25 and 100 is
300

(Three hundred)

300 is the smallest positive integer that 15, 25 and 100 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 25 and 100 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 15: 3 × 5 (exponent form: 3 × 5)

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

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

Prime factor1525100Highest power
2——2222
33——3
55525252

LCM = 22 × 3 × 52 = 300

Checking the LCM of 15, 25 and 100 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(15, 25) = (15 × 25) ÷ 5 = 375 ÷ 5 = 75

LCM(75, 100) = (75 × 100) ÷ 25 = 7,500 ÷ 25 = 300

LCM(15, 25, 100) = 300

The pairs may be taken in any order — 25 and 100 first, then 15 — and the answer is the same 300. That is exactly why the two routes on this page agree.

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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 15, 25 and 100? (The answer is: 300). Enter the first number (e.g. '15'), the second (e.g. '25') and the third (e.g. '100'), 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
1525851,275
1525866,450
1525872,175
1525886,600
1525896,675
152590450
1525916,825
1525926,900
1525932,325
1525947,050
1525951,425
1525962,400
1525977,275
1525987,350
1525992,475
1525100300
15251017,575
15251022,550
15251037,725
15251047,800
1525105525
15251067,950
15251078,025
15251082,700
15251098,175
15251101,650
15251112,775
15251128,400
15251138,475
15251142,850

FAQ

What's the Least Common Multiple (LCM) of 15, 25 and 100?

LCM of 15, 25 and 100 is 300

How to find the LCM of 15, 25 and 100 by prime factorization?

Take every prime that appears in 15, 25 and 100 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 15, 25 and 100 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 25 is 75, and the LCM of 75 and 100 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 15, 25 and 100?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 15, 300 ÷ 25 and 300 ÷ 100 all come out whole. Any other common multiple of 15, 25 and 100 is a multiple of 300.

See Also