LCM of 21 and 97 is 2037. The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 21 and 97, 2037 is the first(least or smallest) number that is common in the set of multiples of 21 and 97. 4074 is also the common multiple of 21 and 97. However 2037 is the smallest. Hence 2037 is the LCM which is also known as LCD, Least Common Divisor for 21 and 97. You can read more on LCM for further details.
What is LCM of 21 and 97
The Least Common Multiple or Lowest Common Multiple of 21 and 97 is 2037.
How to Find LCM of 21 and 97?
LCM of 21 and 97 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 97 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 21 and 97 can be expressed as;
21 = 3 × 7
97 = 1 × 97
LCM (21, 97) = 3 × 7 × 97 = 2037
LCM of 21 and 97 Using Division Method
In the Division Method, the numbers 21 and 97 are divided by prime divisors. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
3 |
21 |
97 |
|
7 |
7 |
97 |
|
97 |
1 |
97 |
|
× |
1 |
1 |
LCM (21, 97) = 3 × 7 × 97 = 2037
LCM of 21 and 97 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 21 and 97
Multiples of 21
21, 42, 63, 84, … 630, 651, 672, 693, 714, 735, …. 1176, 1197, 1218, … 1596, 1617, …, 1827, 1848, …, 1974, 1995, 2016, 2037, 2058, 2079
Multiples of 97
97, 194, 291, 388, 485, 582, 679, …1261, 1358, 1455, … 1843, 1940, 2037, 2134, 2231
LCM (21, 97) = 2037
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 21 and 97?
Answer: 2037 is the smallest number that is divisible by both 21 and 97.
What is the LCM for 7, 21 and 97?
Answer: LCM for 7, 21 and 97 is 2037 as 7 is the prime factor of 21.
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