LCM for 10, 20 and 30

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

What's the Least Common Multiple (LCM) of 10, 20 and 30?

Answer

LCM of 10, 20 and 30 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 10 = 6, 60 ÷ 20 = 3, 60 ÷ 30 = 2 — and 6, 3 and 2 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/10 by 6 and of y/20 by 3 and of z/30 by 2.

10 = 2 × 5

20 = 22 × 5

30 = 2 × 3 × 5

Prime102030Highest power
2222222
3——33
55555

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

LCM = 22 × 3 × 5 = 60

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
10152060
10162080
101720340
101820180
101920380
10202020
102021420
102022220
102023460
102024120
102025100
102026260
102027540
102028140
102029580
10203060
102031620
102032160
102033660
102034340
102035140
102036180
102037740
102038380
102039780
10204040
102041820
102042420
102043860
102044220

FAQ

What's the Least Common Multiple (LCM) of 10, 20 and 30?

LCM of 10, 20 and 30 is 60

How to find the LCM of 10, 20 and 30 by prime factorization?

Take every prime that appears in 10, 20 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 10, 20 and 30 two numbers at a time?

Yes. The LCM of 10 and 20 is 20, and the LCM of 20 and 30 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 10, 20 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 10, 60 ÷ 20 and 60 ÷ 30 all come out whole. Any other common multiple of 10, 20 and 30 is a multiple of 60.

See Also