Least Common Multiple (LCM) of 157 and 117
The least common multiple (LCM) of 157 and 117 is 18369.
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 157 and 117?
First, calculate the GCD of 157 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 117 = 1 remainder 40 |
| 2 | 117 ÷ 40 = 2 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 25 | 1725 |
| 114 and 192 | 3648 |
| 116 and 121 | 14036 |
| 112 and 68 | 1904 |
| 54 and 145 | 7830 |