LCM for 12, 36 and 48

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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

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 12 = 12, 144 ÷ 36 = 4, 144 ÷ 48 = 3 — and 12, 4 and 3 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/12 by 12 and of y/36 by 4 and of z/48 by 3.

12 = 22 × 3

36 = 22 × 32

48 = 24 × 3

Prime123648Highest power
222222424
3332332

LCM = 24 × 32 = 144

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See Also

LCM Table

1st2nd3rdLCM
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. 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