LCM for 84 and 105

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What's the Least Common Multiple (LCM) of 84 and 105?

Answer

LCM of 84 and 105 is
420

(Four hundred twenty)

Finding LCM for 84 and 105 using GCF of these numbers

The first method to find LCM for numbers 84 and 105 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 84 and 105 is 21, so

LCM = (84 × 105) ÷ 21

LCM = 8,820 ÷ 21

LCM = 420

Finding LCM for 84 and 105 by Listing Multiples

The second method to find LCM for numbers 84 and 105 is to list out the common multiples for both numbers and pick the first one that matches:

Multiples of 84: 84, 168, 252, 336, 420, 504, 588

Multiples of 105: 105, 210, 315, 420, 525, 630

So the LCM for 84 and 105 is 420

Finding LCM for 84 and 105 by Prime Factorization

Another method to find LCM for numbers 84 and 105 is to list all Prime Factors for both numbers and multiply the highest exponent prime factors:

All Prime Factors of 84: 2, 2, 3, 7 (exponent form: 22, 31, 71)

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

22 × 31 × 71 × 51 = 420

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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 84 and 105? (The answer is: 420). Select the first number (e.g. '84') 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
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LCM Table

Number 1Number 2LCM
84901,260
84911,092
84921,932
84932,604
84943,948
84957,980
8496672
84978,148
8498588
84992,772
841002,100
841018,484
841021,428
841038,652
841042,184
84105420
841064,452
841078,988
84108756
841099,156
841104,620
841113,108
84112336
841139,492
841141,596
841159,660
841162,436
841173,276
841184,956
841191,428

FAQ

What's the Least Common Multiple (LCM) of 84 and 105?

LCM of 84 and 105 is 420

How to find the LCM of 84 and 105 using prime factorization?

To find the LCM of 84 and 105, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 420.

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 84 and 105: LCM = 420, GCF = 21.

See Also