Least Common Multiple (LCM) of 53 and 117
The least common multiple (LCM) of 53 and 117 is 6201.
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 117?
First, calculate the GCD of 53 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 117 = 0 remainder 53 |
| 2 | 117 ÷ 53 = 2 remainder 11 |
| 3 | 53 ÷ 11 = 4 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 160 | 1440 |
| 120 and 135 | 1080 |
| 66 and 31 | 2046 |
| 140 and 37 | 5180 |
| 150 and 69 | 3450 |