LCM for 48, 64 and 88

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 48, 64 and 88?

Answer

LCM of 48, 64 and 88 is
2,112

(Two thousand one hundred twelve)

2,112 is the smallest positive integer that 48, 64 and 88 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 48, 64 and 88 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 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

All Prime Factors of 88: 2 × 2 × 2 × 11 (exponent form: 23 × 11)

Prime factor486488Highest power
224262326
33——3
11——1111

LCM = 26 × 3 × 11 = 2,112

Checking the LCM of 48, 64 and 88 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(48, 64) = (48 × 64) ÷ 16 = 3,072 ÷ 16 = 192

LCM(192, 88) = (192 × 88) ÷ 8 = 16,896 ÷ 8 = 2,112

LCM(48, 64, 88) = 2,112

The pairs may be taken in any order — 64 and 88 first, then 48 — and the answer is the same 2,112. 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 48, 64 and 88? (The answer is: 2,112). Enter the first number (e.g. '48'), the second (e.g. '64') and the third (e.g. '88'), 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
48647314,016
4864747,104
4864754,800
4864763,648
48647714,784
4864782,496
48647915,168
486480960
4864815,184
4864827,872
48648315,936
4864841,344
48648516,320
4864868,256
4864875,568
4864882,112
48648917,088
4864902,880
48649117,472
4864924,416
4864935,952
4864949,024
48649518,240
486496192
48649718,624
4864989,408
4864996,336
48641004,800
486410119,392
48641023,264

FAQ

What's the Least Common Multiple (LCM) of 48, 64 and 88?

LCM of 48, 64 and 88 is 2,112

How to find the LCM of 48, 64 and 88 by prime factorization?

Take every prime that appears in 48, 64 and 88 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 × 11 = 2,112.

Can you get the LCM of 48, 64 and 88 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 48 and 64 is 192, and the LCM of 192 and 88 is 2,112 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 2,112 divisible by 48, 64 and 88?

Yes, and by definition it is the smallest positive integer that is: 2,112 ÷ 48, 2,112 ÷ 64 and 2,112 ÷ 88 all come out whole. Any other common multiple of 48, 64 and 88 is a multiple of 2,112.

See Also