LCM for 30, 40 and 50

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

What's the Least Common Multiple (LCM) of 30, 40 and 50?

Answer

LCM of 30, 40 and 50 is
600

(Six hundred)

600 is the smallest positive integer that 30, 40 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 30, 40 and 50 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

Prime factor304050Highest power
2223223
33——3
5555252

LCM = 23 × 3 × 52 = 600

Checking the LCM of 30, 40 and 50 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(30, 40) = (30 × 40) ÷ 10 = 1,200 ÷ 10 = 120

LCM(120, 50) = (120 × 50) ÷ 10 = 6,000 ÷ 10 = 600

LCM(30, 40, 50) = 600

The pairs may be taken in any order — 40 and 50 first, then 30 — and the answer is the same 600. 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 30, 40 and 50? (The answer is: 600). Enter the first number (e.g. '30'), the second (e.g. '40') and the third (e.g. '50'), 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
303540840
303640360
3037404,440
3038402,280
3039401,560
304040120
3040414,920
304042840
3040435,160
3040441,320
304045360
3040462,760
3040475,640
304048240
3040495,880
304050600
3040512,040
3040521,560
3040536,360
3040541,080
3040551,320
304056840
3040572,280
3040583,480
3040597,080
304060120
3040617,320
3040623,720
3040632,520
304064960

FAQ

What's the Least Common Multiple (LCM) of 30, 40 and 50?

LCM of 30, 40 and 50 is 600

How to find the LCM of 30, 40 and 50 by prime factorization?

Take every prime that appears in 30, 40 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 30, 40 and 50 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 30 and 40 is 120, and the LCM of 120 and 50 is 600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 600 divisible by 30, 40 and 50?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 30, 600 ÷ 40 and 600 ÷ 50 all come out whole. Any other common multiple of 30, 40 and 50 is a multiple of 600.

See Also