Least Common Multiple (LCM) of 147 and 54
The least common multiple (LCM) of 147 and 54 is 2646.
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 147 and 54?
First, calculate the GCD of 147 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 54 = 2 remainder 39 |
| 2 | 54 ÷ 39 = 1 remainder 15 |
| 3 | 39 ÷ 15 = 2 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 113 | 20905 |
| 40 and 23 | 920 |
| 113 and 117 | 13221 |
| 24 and 192 | 192 |
| 97 and 180 | 17460 |