LCM for 10, 20 and 50

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What's the Least Common Multiple (LCM) of 10, 20 and 50?

Answer

LCM of 10, 20 and 50 is
100

First common multiples: 100, 200, 300, …

100 is divisible by all three: 100 ÷ 10 = 10, 100 ÷ 20 = 5, 100 ÷ 50 = 2 — and 10, 5 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 10 and of y/20 by 5 and of z/50 by 2.

10 = 2 × 5

20 = 22 × 5

50 = 2 × 52

Prime102050Highest power
2222222
5555252

LCM = 22 × 52 = 100

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LCM Table

1st2nd3rdLCM
102035140
102036180
102037740
102038380
102039780
10204040
102041820
102042420
102043860
102044220
102045180
102046460
102047940
102048240
102049980
102050100
1020511,020
102052260
1020531,060
102054540
102055220
102056280
1020571,140
102058580
1020591,180
10206060
1020611,220
102062620
1020631,260
102064320

FAQ

What's the Least Common Multiple (LCM) of 10, 20 and 50?

LCM of 10, 20 and 50 is 100

How to find the LCM of 10, 20 and 50 by prime factorization?

Take every prime that appears in 10, 20 and 50 to the highest power it reaches in any one of them and multiply: 2² × 5² = 100.

Can you get the LCM of 10, 20 and 50 two numbers at a time?

Yes. The LCM of 10 and 20 is 20, and the LCM of 20 and 50 is 100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 100 divisible by 10, 20 and 50?

Yes, and by definition it is the smallest positive integer that is: 100 ÷ 10, 100 ÷ 20 and 100 ÷ 50 all come out whole. Any other common multiple of 10, 20 and 50 is a multiple of 100.

See Also