LCM for 30 and 75

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 30 and 75?

Answer

LCM of 30 and 75 is
150

(One hundred fifty)

Finding LCM for 30 and 75 using GCF of these numbers

The first method to find LCM for numbers 30 and 75 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 30 and 75 is 15, so

LCM = (30 × 75) ÷ 15

LCM = 2,250 ÷ 15

LCM = 150

Finding LCM for 30 and 75 by Listing Multiples

The second method to find LCM for numbers 30 and 75 is to list out the common multiples for both numbers and pick the first one that matches:

Multiples of 30: 30, 60, 90, 120, 150, 180, 210

Multiples of 75: 75, 150, 225, 300

So the LCM for 30 and 75 is 150

Finding LCM for 30 and 75 by Prime Factorization

Another method to find LCM for numbers 30 and 75 is to list all Prime Factors for both numbers and multiply the highest exponent prime factors:

All Prime Factors of 30: 2, 3, 5 (exponent form: 21, 31, 51)

All Prime Factors of 75: 3, 5, 5 (exponent form: 31, 52)

21 × 31 × 52 = 150

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About "Least Common Multiple" Calculator

This calculator will help you find the Least Common Multiple (LCM) of two numbers. For example, it can help you find out what's the Least Common Multiple (LCM) of 30 and 75? (The answer is: 150). Select the first number (e.g. '30') and the second number (e.g. '75'). After that hit the 'Calculate' button.
Least Common Multiple (LCM) also known as the Lowest Common Multiple or Smallest Common Multiple of 2 numbers - it is the smallest positive integer that is divisible by both numbers
"Least Common Multiple" Calculator
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LCM Table

Number 1Number 2LCM
3036180
30371,110
3038570
3040120
3042210
30431,290
304590
3046690
3050150
3055330
3056840
3057570
3058870
306060
3070210
3075150
3096480
30100300
30105210
30110330
30120120
30145870
30155930
30165330
30170510
30180180
301851,110
30195390
302151,290
30225450

FAQ

What's the Least Common Multiple (LCM) of 30 and 75?

LCM of 30 and 75 is 150

How to find the LCM of 30 and 75 using prime factorization?

To find the LCM of 30 and 75, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 150.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 30 and 75: LCM = 150, GCF = 15.

See Also