LCM for 12, 30 and 40

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

What's the Least Common Multiple (LCM) of 12, 30 and 40?

Answer

LCM of 12, 30 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 12 = 10, 120 ÷ 30 = 4, 120 ÷ 40 = 3 — and 10, 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 10 and of y/30 by 4 and of z/40 by 3.

12 = 22 × 3

30 = 2 × 3 × 5

40 = 23 × 5

Prime123040Highest power
22222323
333—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
122530300
122630780
122730540
122830420
1229301,740
12303060
1230311,860
123032480
123033660
1230341,020
123035420
123036180
1230372,220
1230381,140
123039780
123040120
1230412,460
123042420
1230432,580
123044660
123045180
1230461,380
1230472,820
123048240
1230492,940
123050300
1230511,020
123052780
1230533,180
123054540

FAQ

What's the Least Common Multiple (LCM) of 12, 30 and 40?

LCM of 12, 30 and 40 is 120

How to find the LCM of 12, 30 and 40 by prime factorization?

Take every prime that appears in 12, 30 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, 30 and 40 two numbers at a time?

Yes. The LCM of 12 and 30 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, 30 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 30 and 120 ÷ 40 all come out whole. Any other common multiple of 12, 30 and 40 is a multiple of 120.

See Also