Least Common Multiple (LCM) of 21 and 108
The least common multiple (LCM) of 21 and 108 is 756.
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 108?
First, calculate the GCD of 21 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 108 = 0 remainder 21 |
| 2 | 108 ÷ 21 = 5 remainder 3 |
| 3 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 78 | 858 |
| 10 and 197 | 1970 |
| 196 and 116 | 5684 |
| 16 and 148 | 592 |
| 72 and 108 | 216 |