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 |
|---|---|
| 108 and 104 | 2808 |
| 200 and 101 | 20200 |
| 115 and 98 | 11270 |
| 115 and 148 | 17020 |
| 141 and 41 | 5781 |