LCM for 30, 36 and 48

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 30, 36 and 48?

Answer

LCM of 30, 36 and 48 is
720

(Seven hundred twenty)

720 is the smallest positive integer that 30, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 30, 36 and 48 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

Prime factor303648Highest power
22222424
3332332
55——5

LCM = 24 × 32 × 5 = 720

Checking the LCM of 30, 36 and 48 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(30, 36) = (30 × 36) ÷ 6 = 1,080 ÷ 6 = 180

LCM(180, 48) = (180 × 48) ÷ 12 = 8,640 ÷ 12 = 720

LCM(30, 36, 48) = 720

The pairs may be taken in any order — 36 and 48 first, then 30 — and the answer is the same 720. That is exactly why the two routes on this page agree.

Related Calculations

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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 30, 36 and 48? (The answer is: 720). Enter the first number (e.g. '30'), the second (e.g. '36') and the third (e.g. '48'), 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
3033361,980
3034363,060
3035361,260
303636180
3036376,660
3036383,420
3036392,340
303640360
3036417,380
3036421,260
3036437,740
3036441,980
303645180
3036464,140
3036478,460
303648720
3036498,820
303650900
3036513,060
3036522,340
3036539,540
303654540
3036551,980
3036562,520
3036573,420
3036585,220
30365910,620
303660180
30366110,980
3036625,580

FAQ

What's the Least Common Multiple (LCM) of 30, 36 and 48?

LCM of 30, 36 and 48 is 720

How to find the LCM of 30, 36 and 48 by prime factorization?

Take every prime that appears in 30, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 30, 36 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 30 and 36 is 180, and the LCM of 180 and 48 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 720 divisible by 30, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 30, 720 ÷ 36 and 720 ÷ 48 all come out whole. Any other common multiple of 30, 36 and 48 is a multiple of 720.

See Also