LCM for 50, 100 and 150

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

What's the Least Common Multiple (LCM) of 50, 100 and 150?

Answer

LCM of 50, 100 and 150 is
300

(Three hundred)

300 is the smallest positive integer that 50, 100 and 150 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 50, 100 and 150 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

All Prime Factors of 150: 2 × 3 × 5 × 5 (exponent form: 2 × 3 × 52)

Prime factor50100150Highest power
2222222
3——33
552525252

LCM = 22 × 3 × 52 = 300

Checking the LCM of 50, 100 and 150 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(50, 100) = (50 × 100) ÷ 50 = 5,000 ÷ 50 = 100

LCM(100, 150) = (100 × 150) ÷ 50 = 15,000 ÷ 50 = 300

LCM(50, 100, 150) = 300

The pairs may be taken in any order — 100 and 150 first, then 50 — and the answer is the same 300. 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 50, 100 and 150? (The answer is: 300). Enter the first number (e.g. '50'), the second (e.g. '100') and the third (e.g. '150'), 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
501001352,700
501001363,400
5010013713,700
501001386,900
5010013913,900
50100140700
5010014114,100
501001427,100
5010014314,300
501001443,600
501001452,900
501001467,300
5010014714,700
501001483,700
5010014914,900
50100150300
5010015115,100
501001523,800
5010015315,300
501001547,700
501001553,100
501001563,900
5010015715,700
501001587,900
5010015915,900
50100160800
5010016116,100
501001628,100
5010016316,300
501001644,100

FAQ

What's the Least Common Multiple (LCM) of 50, 100 and 150?

LCM of 50, 100 and 150 is 300

How to find the LCM of 50, 100 and 150 by prime factorization?

Take every prime that appears in 50, 100 and 150 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 50, 100 and 150 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 50 and 100 is 100, and the LCM of 100 and 150 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 50, 100 and 150?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 50, 300 ÷ 100 and 300 ÷ 150 all come out whole. Any other common multiple of 50, 100 and 150 is a multiple of 300.

See Also