LCM for 39, 45 and 54

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

What's the Least Common Multiple (LCM) of 39, 45 and 54?

Answer

LCM of 39, 45 and 54 is
3,510

First common multiples: 3,510; 7,020; 10,530; …

3,510 is divisible by all three: 3,510 ÷ 39 = 90; 3,510 ÷ 45 = 78; 3,510 ÷ 54 = 65 — and 90, 78 and 65 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/39 by 90 and of y/45 by 78 and of z/54 by 65.

39 = 3 × 13

45 = 32 × 5

54 = 2 × 33

Prime394554Highest power
2——22
33323333
5—5—5
1313——13

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

LCM = 2 × 33 × 5 × 13 = 3,510

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
393945585
3940454,680
39414523,985
3942458,190
39434525,155
39444525,740
394545585
39454626,910
39454727,495
3945489,360
39454928,665
3945505,850
3945519,945
3945522,340
39455331,005
3945543,510
3945556,435
39455632,760
39455711,115
39455833,930
39455934,515
3945602,340
39456135,685
39456236,270
3945634,095
39456437,440
394565585
39456612,870
39456739,195
39456839,780

FAQ

What's the Least Common Multiple (LCM) of 39, 45 and 54?

LCM of 39, 45 and 54 is 3,510

How to find the LCM of 39, 45 and 54 by prime factorization?

Take every prime that appears in 39, 45 and 54 to the highest power it reaches in any one of them and multiply: 2 × 3³ × 5 × 13 = 3,510.

Can you get the LCM of 39, 45 and 54 two numbers at a time?

Yes. The LCM of 39 and 45 is 585, and the LCM of 585 and 54 is 3,510 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,510 divisible by 39, 45 and 54?

Yes, and by definition it is the smallest positive integer that is: 3,510 ÷ 39, 3,510 ÷ 45 and 3,510 ÷ 54 all come out whole. Any other common multiple of 39, 45 and 54 is a multiple of 3,510.

See Also