LCM for 16, 48 and 64

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 16, 48 and 64?

Answer

LCM of 16, 48 and 64 is
192

(One hundred ninety-two)

192 is the smallest positive integer that 16, 48 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 48 and 64 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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)

Prime factor164864Highest power
224242626
3—3—3

LCM = 26 × 3 = 192

Checking the LCM of 16, 48 and 64 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(16, 48) = (16 × 48) ÷ 16 = 768 ÷ 16 = 48

LCM(48, 64) = (48 × 64) ÷ 16 = 3,072 ÷ 16 = 192

LCM(16, 48, 64) = 192

The pairs may be taken in any order — 48 and 64 first, then 16 — and the answer is the same 192. 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 16, 48 and 64? (The answer is: 192). Enter the first number (e.g. '16'), the second (e.g. '48') and the third (e.g. '64'), 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
1648492,352
1648501,200
164851816
164852624
1648532,544
164854432
1648552,640
164856336
164857912
1648581,392
1648592,832
164860240
1648612,928
1648621,488
1648631,008
164864192
1648653,120
164866528
1648673,216
164868816
1648691,104
1648701,680
1648713,408
164872144
1648733,504
1648741,776
1648751,200
164876912
1648773,696
164878624

FAQ

What's the Least Common Multiple (LCM) of 16, 48 and 64?

LCM of 16, 48 and 64 is 192

How to find the LCM of 16, 48 and 64 by prime factorization?

Take every prime that appears in 16, 48 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

Can you get the LCM of 16, 48 and 64 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 48 is 48, and the LCM of 48 and 64 is 192 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 192 divisible by 16, 48 and 64?

Yes, and by definition it is the smallest positive integer that is: 192 ÷ 16, 192 ÷ 48 and 192 ÷ 64 all come out whole. Any other common multiple of 16, 48 and 64 is a multiple of 192.

See Also