Least Common Multiple (LCM) of 118 and 65
The least common multiple (LCM) of 118 and 65 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 118 and 65?
First, calculate the GCD of 118 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 65 = 1 remainder 53 |
| 2 | 65 ÷ 53 = 1 remainder 12 |
| 3 | 53 ÷ 12 = 4 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 20 | 780 |
| 100 and 106 | 5300 |
| 90 and 103 | 9270 |
| 137 and 198 | 27126 |
| 111 and 113 | 12543 |