LCM for 60, 75 and 111

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 60, 75 and 111?

Answer

LCM of 60, 75 and 111 is
11,100

(Eleven thousand one hundred)

11,100 is the smallest positive integer that 60, 75 and 111 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 60, 75 and 111 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 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

All Prime Factors of 111: 3 × 37 (exponent form: 3 × 37)

Prime factor6075111Highest power
222——22
33333
5552—52
37——3737

LCM = 22 × 3 × 52 × 37 = 11,100

Checking the LCM of 60, 75 and 111 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(60, 75) = (60 × 75) ÷ 15 = 4,500 ÷ 15 = 300

LCM(300, 111) = (300 × 111) ÷ 3 = 33,300 ÷ 3 = 11,100

LCM(60, 75, 111) = 11,100

The pairs may be taken in any order — 75 and 111 first, then 60 — and the answer is the same 11,100. 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 60, 75 and 111? (The answer is: 11,100). Enter the first number (e.g. '60'), the second (e.g. '75') and the third (e.g. '111'), 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
6075962,400
60759729,100
60759814,700
6075999,900
6075100300
607510130,300
60751025,100
607510330,900
60751047,800
60751052,100
607510615,900
607510732,100
60751082,700
607510932,700
60751103,300
607511111,100
60751128,400
607511333,900
60751145,700
60751156,900
60751168,700
607511711,700
607511817,700
607511935,700
6075120600
607512136,300
607512218,300
607512312,300
60751249,300
60751251,500

FAQ

What's the Least Common Multiple (LCM) of 60, 75 and 111?

LCM of 60, 75 and 111 is 11,100

How to find the LCM of 60, 75 and 111 by prime factorization?

Take every prime that appears in 60, 75 and 111 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² × 37 = 11,100.

Can you get the LCM of 60, 75 and 111 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 60 and 75 is 300, and the LCM of 300 and 111 is 11,100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 11,100 divisible by 60, 75 and 111?

Yes, and by definition it is the smallest positive integer that is: 11,100 ÷ 60, 11,100 ÷ 75 and 11,100 ÷ 111 all come out whole. Any other common multiple of 60, 75 and 111 is a multiple of 11,100.

See Also