Least Common Multiple (LCM) of 53 and 118
The least common multiple (LCM) of 53 and 118 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 53 and 118?
First, calculate the GCD of 53 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 118 = 0 remainder 53 |
| 2 | 118 ÷ 53 = 2 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 |
|---|---|
| 160 and 105 | 3360 |
| 190 and 133 | 1330 |
| 43 and 27 | 1161 |
| 131 and 17 | 2227 |
| 96 and 180 | 1440 |