LCM of 7, 8, 14 and 21 is 168. LCM is the short form for Least Common Multiple or the Lowest common multiple, also known as LCD Least Common Divisor. LCM/LCD (Here 168) is the positive integer that is a common multiple of the given set of numbers(here 7,8, 14 and 21). Here the given set of numbers are 7, 8, 14 and 21. The smallest common multiple for all these numbers among many is 168, and hence it is the LCM. 336, 504, 672 are also the common multiples. You can refer to Multiples.
What is LCM of 7, 8, 14 and 21
The Least Common Multiple or Lowest Common Multiple of 7, 8, 14 and 21 is 168.
How to Find LCM of 7, 8, 14 and 21 ?
LCM of 7, 8, 14 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7, 8, 14 and 21 Using Prime Factorisation Method
In the Prime Factorisation method 7, 8, 14 and 21 can be expressed as;
7 = 1 x 7
8 = 2 x 2 x 2
14 = 2 x 7
21 = 3 x 7
The common and uncommon prime factors of 7, 8, 14 and 21 and their product forms the LCM
LCM (7, 8, 14 and 21) = 2 x 2 x 2 x 3 x 7 = 168
LCM of 7, 8, 14 and 21 Using Division Method
In the Division Method, the given set of numbers 7, 8, 14 and 21 are divided using the prime divisors. The division is complete only if the remainders are one. The prime divisors are chosen as the prime numbers in increasing order of divisibility. The product of the prime divisors will be the LCM.
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LCM (7, 8, 14 and 21) = 2 x 2 x 2 x 3 x 7 = 168
LCM of 7, 8, 14 and 21 Using Listing the Multiples
By listing all the multiples of 7, 8, 14 and 21, we can identify the first common multiple, which is the LCM. Below is the list of multiples for 7, 8, 14 and 21
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182
Multiples of 8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184
Multiples of 14
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196
Multiples of 21
21, 42, 63, 84, 105, 126, 147, 168, 189, 210
LCM (7, 8, 14 and 21) = 168
Related Articles
- LCM
- HCF and LCM
- LCM Formula
- LCM Calculator
- Prime Factorization and Division method
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 7, 8, 14 and 21?
Answer: 168 is the smallest number that is divisible by 7, 8, 14 and 21 .
What is the LCM of 3 and 168?
Answer: LCM of 3 and 168 is 168.
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