LCM for 10, 22 and 99

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What's the Least Common Multiple (LCM) of 10, 22 and 99?

Answer

LCM of 10, 22 and 99 is
990

First common multiples: 990; 1,980; 2,970; …

990 is divisible by all three: 990 ÷ 10 = 99, 990 ÷ 22 = 45, 990 ÷ 99 = 10 — and 99, 45 and 10 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 99 and of y/22 by 45 and of z/99 by 10.

10 = 2 × 5

22 = 2 × 11

99 = 32 × 11

Prime102299Highest power
222—2
3——3232
55——5
11—111111

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

LCM = 2 × 32 × 5 × 11 = 990

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LCM Table

1st2nd3rdLCM
1022844,620
1022851,870
1022864,730
1022879,570
102288440
1022899,790
102290990
10229110,010
1022925,060
10229310,230
1022945,170
1022952,090
1022965,280
10229710,670
1022985,390
102299990
10221001,100
102210111,110
10221025,610
102210311,330
10221045,720
10221052,310
10221065,830
102210711,770
10221085,940
102210911,990
1022110110
102211112,210
10221126,160
102211312,430

FAQ

What's the Least Common Multiple (LCM) of 10, 22 and 99?

LCM of 10, 22 and 99 is 990

How to find the LCM of 10, 22 and 99 by prime factorization?

Take every prime that appears in 10, 22 and 99 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 11 = 990.

Can you get the LCM of 10, 22 and 99 two numbers at a time?

Yes. The LCM of 10 and 22 is 110, and the LCM of 110 and 99 is 990 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 990 divisible by 10, 22 and 99?

Yes, and by definition it is the smallest positive integer that is: 990 ÷ 10, 990 ÷ 22 and 990 ÷ 99 all come out whole. Any other common multiple of 10, 22 and 99 is a multiple of 990.

See Also