Least Common Multiple (LCM) of 118 and 52
The least common multiple (LCM) of 118 and 52 is 3068.
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 52?
First, calculate the GCD of 118 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 52 = 2 remainder 14 |
| 2 | 52 ÷ 14 = 3 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 135 | 2160 |
| 112 and 98 | 784 |
| 138 and 85 | 11730 |
| 163 and 105 | 17115 |
| 52 and 149 | 7748 |