LCM for 8, 18 and 24

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

What's the Least Common Multiple (LCM) of 8, 18 and 24?

Answer

LCM of 8, 18 and 24 is
72

(Seventy-two)

72 is the smallest positive integer that 8, 18 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 18 and 24 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

Prime factor81824Highest power
22322323
3—32332

LCM = 23 × 32 = 72

Checking the LCM of 8, 18 and 24 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(8, 18) = (8 × 18) ÷ 2 = 144 ÷ 2 = 72

LCM(72, 24) = (72 × 24) ÷ 24 = 1,728 ÷ 24 = 72

LCM(8, 18, 24) = 72

The pairs may be taken in any order — 18 and 24 first, then 8 — and the answer is the same 72. That is exactly why the two routes on this page agree.

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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 8, 18 and 24? (The answer is: 72). Enter the first number (e.g. '8'), the second (e.g. '18') and the third (e.g. '24'), 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
891872
81018360
81118792
8121872
81318936
81418504
81518360
81618144
817181,224
8181872
818191,368
81820360
81821504
81822792
818231,656
8182472
818251,800
81826936
81827216
81828504
818292,088
81830360
818312,232
81832288
81833792
818341,224
818352,520
8183672
818372,664
818381,368

FAQ

What's the Least Common Multiple (LCM) of 8, 18 and 24?

LCM of 8, 18 and 24 is 72

How to find the LCM of 8, 18 and 24 by prime factorization?

Take every prime that appears in 8, 18 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 8, 18 and 24 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 18 is 72, and the LCM of 72 and 24 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 8, 18 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 18 and 72 ÷ 24 all come out whole. Any other common multiple of 8, 18 and 24 is a multiple of 72.

See Also