LCM for 45 and 105

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What's the Least Common Multiple (LCM) of 45 and 105?

Answer

LCM of 45 and 105 is
315

(Three hundred fifteen)

Finding LCM for 45 and 105 using GCF of these numbers

The first method to find LCM for numbers 45 and 105 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 45 and 105 is 15, so

LCM = (45 × 105) ÷ 15

LCM = 4,725 ÷ 15

LCM = 315

Finding LCM for 45 and 105 by Listing Multiples

The second method to find LCM for numbers 45 and 105 is to list out the common multiples for both numbers and pick the first one that matches:

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405

Multiples of 105: 105, 210, 315, 420, 525

So the LCM for 45 and 105 is 315

Finding LCM for 45 and 105 by Prime Factorization

Another method to find LCM for numbers 45 and 105 is to list all Prime Factors for both numbers and multiply the highest exponent prime factors:

All Prime Factors of 45: 3, 3, 5 (exponent form: 32, 51)

All Prime Factors of 105: 3, 5, 7 (exponent form: 31, 51, 71)

32 × 51 × 71 = 315

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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 45 and 105? (The answer is: 315). Select the first number (e.g. '45') 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
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LCM Table

Number 1Number 2LCM
45462,070
45492,205
4550450
45522,340
45532,385
4554270
4555495
4557855
4560180
4563315
4565585
4570630
4575225
45763,420
4580720
4581405
45841,260
459090
4595855
4599495
45100900
45105315
45108540
45117585
45120360
451251,125
45135135
45150450
45180180
45405405

FAQ

What's the Least Common Multiple (LCM) of 45 and 105?

LCM of 45 and 105 is 315

How to find the LCM of 45 and 105 using prime factorization?

To find the LCM of 45 and 105, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 315.

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 45 and 105: LCM = 315, GCF = 15.

See Also