Least Common Multiple (LCM) of 118 and 53
The least common multiple (LCM) of 118 and 53 is 6254.
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 53?
First, calculate the GCD of 118 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 53 = 2 remainder 12 |
| 2 | 53 ÷ 12 = 4 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 144 | 2448 |
| 189 and 73 | 13797 |
| 65 and 20 | 260 |
| 133 and 35 | 665 |
| 70 and 11 | 770 |