LCM for 18, 42 and 48

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

What's the Least Common Multiple (LCM) of 18, 42 and 48?

Answer

LCM of 18, 42 and 48 is
1,008

(One thousand eight)

1,008 is the smallest positive integer that 18, 42 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 42 and 48 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

Prime factor184248Highest power
2222424
3323332
7—7—7

LCM = 24 × 32 × 7 = 1,008

Checking the LCM of 18, 42 and 48 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(18, 42) = (18 × 42) ÷ 6 = 756 ÷ 6 = 126

LCM(126, 48) = (126 × 48) ÷ 6 = 6,048 ÷ 6 = 1,008

LCM(18, 42, 48) = 1,008

The pairs may be taken in any order — 42 and 48 first, then 18 — and the answer is the same 1,008. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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 18, 42 and 48? (The answer is: 1,008). Enter the first number (e.g. '18'), the second (e.g. '42') and the third (e.g. '48'), 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
1833421,386
1834422,142
183542630
183642252
1837424,662
1838422,394
1839421,638
1840422,520
1841425,166
184242126
1842435,418
1842442,772
184245630
1842462,898
1842475,922
1842481,008
184249882
1842503,150
1842512,142
1842523,276
1842536,678
184254378
1842556,930
184256504
1842572,394
1842583,654
1842597,434
1842601,260
1842617,686
1842623,906

FAQ

What's the Least Common Multiple (LCM) of 18, 42 and 48?

LCM of 18, 42 and 48 is 1,008

How to find the LCM of 18, 42 and 48 by prime factorization?

Take every prime that appears in 18, 42 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 7 = 1,008.

Can you get the LCM of 18, 42 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 42 is 126, and the LCM of 126 and 48 is 1,008 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,008 divisible by 18, 42 and 48?

Yes, and by definition it is the smallest positive integer that is: 1,008 ÷ 18, 1,008 ÷ 42 and 1,008 ÷ 48 all come out whole. Any other common multiple of 18, 42 and 48 is a multiple of 1,008.

See Also