Least Common Multiple (LCM) of 108 and 147
The least common multiple (LCM) of 108 and 147 is 5292.
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 108 and 147?
First, calculate the GCD of 108 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 147 = 0 remainder 108 |
| 2 | 147 ÷ 108 = 1 remainder 39 |
| 3 | 108 ÷ 39 = 2 remainder 30 |
| 4 | 39 ÷ 30 = 1 remainder 9 |
| 5 | 30 ÷ 9 = 3 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 16 | 80 |
| 181 and 80 | 14480 |
| 170 and 54 | 4590 |
| 120 and 82 | 4920 |
| 152 and 93 | 14136 |