Least Common Multiple (LCM) of 157 and 168
The least common multiple (LCM) of 157 and 168 is 26376.
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 168?
First, calculate the GCD of 157 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 168 = 0 remainder 157 |
| 2 | 168 ÷ 157 = 1 remainder 11 |
| 3 | 157 ÷ 11 = 14 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 72 | 7416 |
| 85 and 49 | 4165 |
| 182 and 69 | 12558 |
| 100 and 14 | 700 |
| 135 and 93 | 4185 |