LCM for 112, 160 and 188

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 112, 160 and 188?

Answer

LCM of 112, 160 and 188 is
52,640

(Fifty-two thousand six hundred forty)

52,640 is the smallest positive integer that 112, 160 and 188 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 112, 160 and 188 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 112: 2 × 2 × 2 × 2 × 7 (exponent form: 24 × 7)

All Prime Factors of 160: 2 × 2 × 2 × 2 × 2 × 5 (exponent form: 25 × 5)

All Prime Factors of 188: 2 × 2 × 47 (exponent form: 22 × 47)

Prime factor112160188Highest power
224252225
5—5—5
77——7
47——4747

LCM = 25 × 5 × 7 × 47 = 52,640

Checking the LCM of 112, 160 and 188 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(112, 160) = (112 × 160) ÷ 16 = 17,920 ÷ 16 = 1,120

LCM(1,120, 188) = (1,120 × 188) ÷ 4 = 210,560 ÷ 4 = 52,640

LCM(112, 160, 188) = 52,640

The pairs may be taken in any order — 160 and 188 first, then 112 — and the answer is the same 52,640. 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 112, 160 and 188? (The answer is: 52,640). Enter the first number (e.g. '112'), the second (e.g. '160') and the third (e.g. '188'), 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
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and

LCM Table

Number 1Number 2Number 3LCM
112160173193,760
11216017497,440
1121601755,600
11216017612,320
112160177198,240
11216017899,680
112160179200,480
11216018010,080
112160181202,720
11216018214,560
112160183204,960
11216018425,760
11216018541,440
112160186104,160
112160187209,440
11216018852,640
11216018930,240
11216019021,280
112160191213,920
1121601926,720
112160193216,160
112160194108,640
11216019543,680
1121601967,840
112160197220,640
112160198110,880
112160199222,880
1121602005,600
112160201225,120
112160202113,120

FAQ

What's the Least Common Multiple (LCM) of 112, 160 and 188?

LCM of 112, 160 and 188 is 52,640

How to find the LCM of 112, 160 and 188 by prime factorization?

Take every prime that appears in 112, 160 and 188 to the highest power it reaches in any one of them and multiply: 2⁵ × 5 × 7 × 47 = 52,640.

Can you get the LCM of 112, 160 and 188 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 112 and 160 is 1,120, and the LCM of 1,120 and 188 is 52,640 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 52,640 divisible by 112, 160 and 188?

Yes, and by definition it is the smallest positive integer that is: 52,640 ÷ 112, 52,640 ÷ 160 and 52,640 ÷ 188 all come out whole. Any other common multiple of 112, 160 and 188 is a multiple of 52,640.

See Also