Least Common Multiple (LCM) of 65 and 147
The least common multiple (LCM) of 65 and 147 is 9555.
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 65 and 147?
First, calculate the GCD of 65 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 147 = 0 remainder 65 |
| 2 | 147 ÷ 65 = 2 remainder 17 |
| 3 | 65 ÷ 17 = 3 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 38 | 2090 |
| 107 and 85 | 9095 |
| 38 and 168 | 3192 |
| 139 and 125 | 17375 |
| 197 and 82 | 16154 |