LCM for 18, 28 and 48

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What's the Least Common Multiple (LCM) of 18, 28 and 48?

Answer

LCM of 18, 28 and 48 is
1,008

First common multiples: 1,008; 2,016; 3,024; …

1,008 is divisible by all three: 1,008 ÷ 18 = 56; 1,008 ÷ 28 = 36; 1,008 ÷ 48 = 21 — and 56, 36 and 21 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/18 by 56 and of y/28 by 36 and of z/48 by 21.

18 = 2 × 32

28 = 22 × 7

48 = 24 × 3

Prime182848Highest power
22222424
332—332
7—7—7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 24 × 32 × 7 = 1,008

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LCM Table

1st2nd3rdLCM
1828332,772
1828344,284
1828351,260
182836252
1828379,324
1828384,788
1828393,276
1828402,520
18284110,332
182842252
18284310,836
1828442,772
1828451,260
1828465,796
18284711,844
1828481,008
1828491,764
1828506,300
1828514,284
1828523,276
18285313,356
182854756
18285513,860
182856504
1828574,788
1828587,308
18285914,868
1828601,260
18286115,372
1828627,812

FAQ

What's the Least Common Multiple (LCM) of 18, 28 and 48?

LCM of 18, 28 and 48 is 1,008

How to find the LCM of 18, 28 and 48 by prime factorization?

Take every prime that appears in 18, 28 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 7 = 1,008.

Can you get the LCM of 18, 28 and 48 two numbers at a time?

Yes. The LCM of 18 and 28 is 252, and the LCM of 252 and 48 is 1,008 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,008 divisible by 18, 28 and 48?

Yes, and by definition it is the smallest positive integer that is: 1,008 ÷ 18, 1,008 ÷ 28 and 1,008 ÷ 48 all come out whole. Any other common multiple of 18, 28 and 48 is a multiple of 1,008.

See Also