LCM for 10, 22 and 99

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

(Nine hundred ninety)

990 is the smallest positive integer that 10, 22 and 99 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 22 and 99 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 22: 2 × 11 (exponent form: 2 × 11)

All Prime Factors of 99: 3 × 3 × 11 (exponent form: 32 × 11)

Prime factor102299Highest power
222—2
3——3232
55——5
11—111111

LCM = 2 × 32 × 5 × 11 = 990

Checking the LCM of 10, 22 and 99 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(10, 22) = (10 × 22) ÷ 2 = 220 ÷ 2 = 110

LCM(110, 99) = (110 × 99) ÷ 11 = 10,890 ÷ 11 = 990

LCM(10, 22, 99) = 990

The pairs may be taken in any order — 22 and 99 first, then 10 — and the answer is the same 990. That is exactly why the two routes on this page agree.

Related Calculations

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 10, 22 and 99? (The answer is: 990). Enter the first number (e.g. '10'), the second (e.g. '22') and the third (e.g. '99'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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