LCM for 15, 30 and 90

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

What's the Least Common Multiple (LCM) of 15, 30 and 90?

Answer

LCM of 15, 30 and 90 is
90

(Ninety)

90 is the smallest positive integer that 15, 30 and 90 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 30 and 90 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 90: 2 × 3 × 3 × 5 (exponent form: 2 × 32 × 5)

Prime factor153090Highest power
2—222
3333232
55555

LCM = 2 × 32 × 5 = 90

Checking the LCM of 15, 30 and 90 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, 30) = (15 × 30) ÷ 15 = 450 ÷ 15 = 30

LCM(30, 90) = (30 × 90) ÷ 30 = 2,700 ÷ 30 = 90

LCM(15, 30, 90) = 90

The pairs may be taken in any order — 30 and 90 first, then 15 — and the answer is the same 90. 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, 30 and 90? (The answer is: 90). Enter the first number (e.g. '15'), the second (e.g. '30') and the third (e.g. '90'), 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
153075150
1530761,140
1530772,310
153078390
1530792,370
153080240
153081810
1530821,230
1530832,490
153084420
153085510
1530861,290
153087870
1530881,320
1530892,670
15309090
1530912,730
1530921,380
153093930
1530941,410
153095570
153096480
1530972,910
1530981,470
153099990
1530100300
15301013,030
1530102510
15301033,090
15301041,560

FAQ

What's the Least Common Multiple (LCM) of 15, 30 and 90?

LCM of 15, 30 and 90 is 90

How to find the LCM of 15, 30 and 90 by prime factorization?

Take every prime that appears in 15, 30 and 90 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 15, 30 and 90 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 30 is 30, and the LCM of 30 and 90 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 15, 30 and 90?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 15, 90 ÷ 30 and 90 ÷ 90 all come out whole. Any other common multiple of 15, 30 and 90 is a multiple of 90.

See Also