Least Common Multiple (LCM) of 65 and 118
The least common multiple (LCM) of 65 and 118 is 7670.
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 118?
First, calculate the GCD of 65 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 118 = 0 remainder 65 |
| 2 | 118 ÷ 65 = 1 remainder 53 |
| 3 | 65 ÷ 53 = 1 remainder 12 |
| 4 | 53 ÷ 12 = 4 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 31 | 1829 |
| 35 and 24 | 840 |
| 119 and 61 | 7259 |
| 134 and 140 | 9380 |
| 64 and 15 | 960 |