LCM of 24 and 84

LCM of 24 and 84 is 168. The Least Common Multiple or Lowest Common Multiple always referred to as LCM is the smallest number that is divisible by the given set of numbers. In the given set of numbers 24 and 84, 168 is the first(least or smallest) number that is common in the set of multiples of 24 and 84. 336 is also the common multiple of 24 and 84. However, 168 is the smallest. Hence 168 is the LCM which is also known as LCD, Least Common Divisor for 24 and 84. You can read more on LCM for further details.

What is LCM of 24 and 84

The Least Common Multiple or Lowest Common Multiple of 24 and 84 is 168.

Lcm Of 24 And 84

How to Find LCM of 24 and 84?

LCM of 24 and 84 can be determined using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 24 and 84 Using Prime Factorisation Method

In the Prime Factorisation method, the numbers 24 and 84 can be expressed as;

24 = 2 × 2 × 2 × 3

84 = 2 × 2 × 3 × 7

The common factors 2 × 2 × 3 along with other factors 2 and 7 are multiplied to get the LCM.

LCM (24, 84) = 2 × 2 × 2 × 3 × 7 = 168

LCM of 24 and 84 Using Division Method

In the Division Method, the given numbers 24 and 84 are divided by common factors. If the division cannot be continued by common factors, other factors are used till the remainder is one. Product of the prime divisors forms the LCM. 

2

24

84

2

12

42

2

6

21

3

3

21

7

1

7

×

1

1

LCM (24, 84) = 2 × 2 × 2 × 3 × 7 = 168

LCM of 24 and 84 Using Listing the Multiples

By listing all the multiples of 24 and 84, we can identify the LCM. Below is the list of multiples for 24 and 84

Multiples of 24

Multiples of 84

24

84

48

168

72

252

96

336

120

420

144

504

168

588

LCM (24, 84) = 168

Related Articles

Video Lesson on Applications of LCM

Solved Examples 

What is the smallest number that is divisible by both 24 and 84?

Answer: 168 is the smallest number that is divisible by both 24 and 84. 

What is the LCM for 2, 3, 24 and 84? 

Answer: LCM for 2, 3, 24 and 84 is 168 as 2 and 3 are the factors of both 24 and 84.

Frequently Asked Questions on LCM of 24 and 84

Q1

What is the LCM of 24 and 84?

The LCM of 24 and 84 is 168.
Q2

Is the LCM of 24 and 84 the same as the Highest Common Factor of 24 and 84?

No. The Least Common Multiple of 24 and 84 is 168 and the Highest Common Factor of 24 and 84 is 3.
Q3

What are the common factors of 24 and 84?

1, 2, 3, 4, 6 and 12 are the common factors of 24 and 84.
Q4

What are the first 3 common multiples of 24 and 84?

The first three common multiples of 24 and 84 are 168, 336, and 504.
Q5

Is the LCM of 6 and 24 the same as the LCM of 16 and 84?

No. LCM of 6 and 24 is 24, whereas the LCM of 16 and 84 is 336. They are not the same.

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