LCM for 12, 20 and 40

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

What's the Least Common Multiple (LCM) of 12, 20 and 40?

Answer

LCM of 12, 20 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 12 = 10, 120 ÷ 20 = 6, 120 ÷ 40 = 3 — and 10, 6 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 10 and of y/20 by 6 and of z/40 by 3.

12 = 22 × 3

20 = 22 × 5

40 = 23 × 5

Prime122040Highest power
222222323
33——3
5—555

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

LCM = 23 × 3 × 5 = 120

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
122025300
122026780
122027540
122028420
1220291,740
12203060
1220311,860
122032480
122033660
1220341,020
122035420
122036180
1220372,220
1220381,140
122039780
122040120
1220412,460
122042420
1220432,580
122044660
122045180
1220461,380
1220472,820
122048240
1220492,940
122050300
1220511,020
122052780
1220533,180
122054540

FAQ

What's the Least Common Multiple (LCM) of 12, 20 and 40?

LCM of 12, 20 and 40 is 120

How to find the LCM of 12, 20 and 40 by prime factorization?

Take every prime that appears in 12, 20 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 12, 20 and 40 two numbers at a time?

Yes. The LCM of 12 and 20 is 60, and the LCM of 60 and 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 12, 20 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 20 and 120 ÷ 40 all come out whole. Any other common multiple of 12, 20 and 40 is a multiple of 120.

See Also