LCM for 62, 93 and 120

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

What's the Least Common Multiple (LCM) of 62, 93 and 120?

Answer

LCM of 62, 93 and 120 is
3,720

(Three thousand seven hundred twenty)

3,720 is the smallest positive integer that 62, 93 and 120 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 62, 93 and 120 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 62: 2 × 31 (exponent form: 2 × 31)

All Prime Factors of 93: 3 × 31 (exponent form: 3 × 31)

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

Prime factor6293120Highest power
22—2323
3—333
5——55
313131—31

LCM = 23 × 3 × 5 × 31 = 3,720

Checking the LCM of 62, 93 and 120 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(62, 93) = (62 × 93) ÷ 31 = 5,766 ÷ 31 = 186

LCM(186, 120) = (186 × 120) ÷ 6 = 22,320 ÷ 6 = 3,720

LCM(62, 93, 120) = 3,720

The pairs may be taken in any order — 93 and 120 first, then 62 — and the answer is the same 3,720. 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 62, 93 and 120? (The answer is: 3,720). Enter the first number (e.g. '62'), the second (e.g. '93') and the third (e.g. '120'), 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
62931056,510
62931069,858
629310719,902
62931083,348
629310920,274
629311010,230
62931116,882
629311210,416
629311321,018
62931143,534
629311521,390
629311610,788
62931177,254
629311810,974
629311922,134
62931203,720
629312122,506
629312211,346
62931237,626
6293124372
629312523,250
62931263,906
629312723,622
629312811,904
62931297,998
629313012,090
629313124,366
62931324,092
629313324,738
629313412,462

FAQ

What's the Least Common Multiple (LCM) of 62, 93 and 120?

LCM of 62, 93 and 120 is 3,720

How to find the LCM of 62, 93 and 120 by prime factorization?

Take every prime that appears in 62, 93 and 120 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 31 = 3,720.

Can you get the LCM of 62, 93 and 120 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 62 and 93 is 186, and the LCM of 186 and 120 is 3,720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,720 divisible by 62, 93 and 120?

Yes, and by definition it is the smallest positive integer that is: 3,720 ÷ 62, 3,720 ÷ 93 and 3,720 ÷ 120 all come out whole. Any other common multiple of 62, 93 and 120 is a multiple of 3,720.

See Also