Least Common Multiple (LCM) of 21 and 11
The least common multiple (LCM) of 21 and 11 is 231.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 21 and 11?
First, calculate the GCD of 21 and 11 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 11 = 1 remainder 10 |
| 2 | 11 ÷ 10 = 1 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 137 | 2740 |
| 107 and 60 | 6420 |
| 114 and 118 | 6726 |
| 126 and 57 | 2394 |
| 48 and 74 | 1776 |