Least Common Multiple (LCM) of 157 and 67
The least common multiple (LCM) of 157 and 67 is 10519.
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 67?
First, calculate the GCD of 157 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 67 = 2 remainder 23 |
| 2 | 67 ÷ 23 = 2 remainder 21 |
| 3 | 23 ÷ 21 = 1 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 191 | 31133 |
| 15 and 180 | 180 |
| 136 and 130 | 8840 |
| 137 and 51 | 6987 |
| 58 and 84 | 2436 |