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.
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.
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