LCM for 60, 75 and 111
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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
First common multiples: 11,100; 22,200; 33,300; …
11,100 is divisible by all three: 11,100 ÷ 60 = 185; 11,100 ÷ 75 = 148; 11,100 ÷ 111 = 100 — and 185, 148 and 100 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/60 by 185 and of y/75 by 148 and of z/111 by 100.
60 = 22 × 3 × 5
75 = 3 × 52
111 = 3 × 37
| Prime | 60 | 75 | 111 | Highest power |
|---|---|---|---|---|
| 2 | 22 | — | — | 22 |
| 3 | 3 | 3 | 3 | 3 |
| 5 | 5 | 52 | — | 52 |
| 37 | — | — | 37 | 37 |
— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.
LCM = 22 × 3 × 52 × 37 = 11,100
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See Also
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
LCM Table
| 1st | 2nd | 3rd | LCM |
|---|---|---|---|
| 60 | 75 | 96 | 2,400 |
| 60 | 75 | 97 | 29,100 |
| 60 | 75 | 98 | 14,700 |
| 60 | 75 | 99 | 9,900 |
| 60 | 75 | 100 | 300 |
| 60 | 75 | 101 | 30,300 |
| 60 | 75 | 102 | 5,100 |
| 60 | 75 | 103 | 30,900 |
| 60 | 75 | 104 | 7,800 |
| 60 | 75 | 105 | 2,100 |
| 60 | 75 | 106 | 15,900 |
| 60 | 75 | 107 | 32,100 |
| 60 | 75 | 108 | 2,700 |
| 60 | 75 | 109 | 32,700 |
| 60 | 75 | 110 | 3,300 |
| 60 | 75 | 111 | 11,100 |
| 60 | 75 | 112 | 8,400 |
| 60 | 75 | 113 | 33,900 |
| 60 | 75 | 114 | 5,700 |
| 60 | 75 | 115 | 6,900 |
| 60 | 75 | 116 | 8,700 |
| 60 | 75 | 117 | 11,700 |
| 60 | 75 | 118 | 17,700 |
| 60 | 75 | 119 | 35,700 |
| 60 | 75 | 120 | 600 |
| 60 | 75 | 121 | 36,300 |
| 60 | 75 | 122 | 18,300 |
| 60 | 75 | 123 | 12,300 |
| 60 | 75 | 124 | 9,300 |
| 60 | 75 | 125 | 1,500 |
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. 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.
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