LCM for 18, 28 and 48

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 18, 28 and 48?

Answer

LCM of 18, 28 and 48 is
1,008

(One thousand eight)

1,008 is the smallest positive integer that 18, 28 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 28 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

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

Prime factor182848Highest power
22222424
332—332
7—7—7

LCM = 24 × 32 × 7 = 1,008

Checking the LCM of 18, 28 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, 28) = (18 × 28) ÷ 2 = 504 ÷ 2 = 252

LCM(252, 48) = (252 × 48) ÷ 12 = 12,096 ÷ 12 = 1,008

LCM(18, 28, 48) = 1,008

The pairs may be taken in any order — 28 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

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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 18, 28 and 48? (The answer is: 1,008). Enter the first number (e.g. '18'), the second (e.g. '28') 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
1828332,772
1828344,284
1828351,260
182836252
1828379,324
1828384,788
1828393,276
1828402,520
18284110,332
182842252
18284310,836
1828442,772
1828451,260
1828465,796
18284711,844
1828481,008
1828491,764
1828506,300
1828514,284
1828523,276
18285313,356
182854756
18285513,860
182856504
1828574,788
1828587,308
18285914,868
1828601,260
18286115,372
1828627,812

FAQ

What's the Least Common Multiple (LCM) of 18, 28 and 48?

LCM of 18, 28 and 48 is 1,008

How to find the LCM of 18, 28 and 48 by prime factorization?

Take every prime that appears in 18, 28 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, 28 and 48 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 28 is 252, and the LCM of 252 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, 28 and 48?

Yes, and by definition it is the smallest positive integer that is: 1,008 ÷ 18, 1,008 ÷ 28 and 1,008 ÷ 48 all come out whole. Any other common multiple of 18, 28 and 48 is a multiple of 1,008.

See Also