LCM for 12, 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 12, 36 and 48?

Answer

LCM of 12, 36 and 48 is
144

(One hundred forty-four)

144 is the smallest positive integer that 12, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

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 factor123648Highest power
222222424
3332332

LCM = 24 × 32 = 144

Checking the LCM of 12, 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(12, 36) = (12 × 36) ÷ 12 = 432 ÷ 12 = 36

LCM(36, 48) = (36 × 48) ÷ 12 = 1,728 ÷ 12 = 144

LCM(12, 36, 48) = 144

The pairs may be taken in any order — 36 and 48 first, then 12 — and the answer is the same 144. 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 12, 36 and 48? (The answer is: 144). Enter the first number (e.g. '12'), 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
123336396
123436612
1235361,260
12363636
1236371,332
123638684
123639468
123640360
1236411,476
123642252
1236431,548
123644396
123645180
123646828
1236471,692
123648144
1236491,764
123650900
123651612
123652468
1236531,908
123654108
1236551,980
123656504
123657684
1236581,044
1236592,124
123660180
1236612,196
1236621,116

FAQ

What's the Least Common Multiple (LCM) of 12, 36 and 48?

LCM of 12, 36 and 48 is 144

How to find the LCM of 12, 36 and 48 by prime factorization?

Take every prime that appears in 12, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 12, 36 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 36 is 36, and the LCM of 36 and 48 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 12, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 36 and 144 ÷ 48 all come out whole. Any other common multiple of 12, 36 and 48 is a multiple of 144.

See Also