LCM for 8, 19 and 23

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

What's the Least Common Multiple (LCM) of 8, 19 and 23?

Answer

LCM of 8, 19 and 23 is
3,496

(Three thousand four hundred ninety-six)

3,496 is the smallest positive integer that 8, 19 and 23 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 19 and 23 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 19: 19 (exponent form: 19)

All Prime Factors of 23: 23 (exponent form: 23)

Prime factor81923Highest power
223——23
19—19—19
23——2323

LCM = 23 × 19 × 23 = 3,496

Checking the LCM of 8, 19 and 23 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, 19) = (8 × 19) ÷ 1 = 152 ÷ 1 = 152

LCM(152, 23) = (152 × 23) ÷ 1 = 3,496 ÷ 1 = 3,496

LCM(8, 19, 23) = 3,496

The pairs may be taken in any order — 19 and 23 first, then 8 — and the answer is the same 3,496. 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, 19 and 23? (The answer is: 3,496). Enter the first number (e.g. '8'), the second (e.g. '19') and the third (e.g. '23'), 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
8819152
89191,368
81019760
811191,672
81219456
813191,976
814191,064
815192,280
81619304
817192,584
818191,368
81919152
81920760
819213,192
819221,672
819233,496
81924456
819253,800
819261,976
819274,104
819281,064
819294,408
819302,280
819314,712
81932608
819335,016
819342,584
819355,320
819361,368
819375,624

FAQ

What's the Least Common Multiple (LCM) of 8, 19 and 23?

LCM of 8, 19 and 23 is 3,496

How to find the LCM of 8, 19 and 23 by prime factorization?

Take every prime that appears in 8, 19 and 23 to the highest power it reaches in any one of them and multiply: 2³ × 19 × 23 = 3,496.

Can you get the LCM of 8, 19 and 23 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 19 is 152, and the LCM of 152 and 23 is 3,496 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,496 divisible by 8, 19 and 23?

Yes, and by definition it is the smallest positive integer that is: 3,496 ÷ 8, 3,496 ÷ 19 and 3,496 ÷ 23 all come out whole. Any other common multiple of 8, 19 and 23 is a multiple of 3,496.

See Also