Least Common Multiple (LCM) of 118 and 68
The least common multiple (LCM) of 118 and 68 is 4012.
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 68?
First, calculate the GCD of 118 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 68 = 1 remainder 50 |
| 2 | 68 ÷ 50 = 1 remainder 18 |
| 3 | 50 ÷ 18 = 2 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 171 | 9063 |
| 15 and 106 | 1590 |
| 75 and 109 | 8175 |
| 156 and 57 | 2964 |
| 96 and 81 | 2592 |