Least Common Multiple (LCM) of 117 and 157
The least common multiple (LCM) of 117 and 157 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 117 and 157?
First, calculate the GCD of 117 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 157 = 0 remainder 117 |
| 2 | 157 ÷ 117 = 1 remainder 40 |
| 3 | 117 ÷ 40 = 2 remainder 37 |
| 4 | 40 ÷ 37 = 1 remainder 3 |
| 5 | 37 ÷ 3 = 12 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 113 | 3390 |
| 141 and 138 | 6486 |
| 48 and 108 | 432 |
| 107 and 46 | 4922 |
| 178 and 33 | 5874 |