LCM for 30 and 105

"Least Common Multiple" Calculator

Least Common Multiple of

and

What's the Least Common Multiple (LCM) of 30 and 105?

Answer

LCM of 30 and 105 is 210

(Two hundred ten)

Finding LCM for 30 and 105 using GCF of these numbers

The first method to find LCM for numbers 30 and 105 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 30 and 105 is 15, so

LCM = (30 × 105) ÷ 15

LCM = 3150 ÷ 15

LCM = 210

Finding LCM for 30 and 105 by Listing Multiples

The second method to find LCM for numbers 30 and 105 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, 240, 270

Multiples of 105: 105, 210, 315, 420

So the LCM for 30 and 105 is 210

Finding LCM for 30 and 105 by Prime Factorization

Another method to find LCM for numbers 30 and 105 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 105: 3, 5, 7 (exponent form: 31, 51, 71)

21 × 31 × 51 × 71 = 210

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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 105? (The answer is: 210). Select the first number (e.g. '30') and the second number (e.g. '105'). 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

Least Common Multiple of

and

LCM Table

Number 1Number 2LCM
15105105
161051680
171051785
18105630
191051995
20105420
21105105
221052310
231052415
24105840
25105525
261052730
27105945
28105420
291053045
30105210
311053255
321053360
331051155
341053570
35105105
361051260
371053885
381053990
391051365
40105840
411054305
42105210
431054515
441054620

FAQ

What's the Least Common Multiple (LCM) of 30 and 105?

LCM of 30 and 105 is 210

How to find the LCM of 30 and 105 using prime factorization?

To find the LCM of 30 and 105, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 210.

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 105: LCM = 210, GCF = 15.

See Also