LCM for 84 and 120

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What's the Least Common Multiple (LCM) of 84 and 120?

Answer

LCM of 84 and 120 is
840

(Eight hundred forty)

Finding LCM for 84 and 120 using GCF of these numbers

The first method to find LCM for numbers 84 and 120 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 84 and 120 is 12, so

LCM = (84 × 120) ÷ 12

LCM = 10,080 ÷ 12

LCM = 840

Finding LCM for 84 and 120 by Listing Multiples

The second method to find LCM for numbers 84 and 120 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, 672, 756, 840, 924, 1,008

Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1,080

So the LCM for 84 and 120 is 840

Finding LCM for 84 and 120 by Prime Factorization

Another method to find LCM for numbers 84 and 120 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 120: 2, 2, 2, 3, 5 (exponent form: 23, 31, 51)

23 × 31 × 71 × 51 = 840

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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 120? (The answer is: 840). Select the first number (e.g. '84') and the second number (e.g. '120'). 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
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LCM Table

Number 1Number 2LCM
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
84120840
8412110,164
841225,124
841233,444
841242,604
8412510,500
84126252
8412710,668
841282,688
841293,612
841305,460
8413111,004
84132924
841331,596
841345,628

FAQ

What's the Least Common Multiple (LCM) of 84 and 120?

LCM of 84 and 120 is 840

How to find the LCM of 84 and 120 using prime factorization?

To find the LCM of 84 and 120, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 840.

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 120: LCM = 840, GCF = 12.

See Also