Least Common Multiple (LCM) of 67 and 157
The least common multiple (LCM) of 67 and 157 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 67 and 157?
First, calculate the GCD of 67 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 157 = 0 remainder 67 |
| 2 | 157 ÷ 67 = 2 remainder 23 |
| 3 | 67 ÷ 23 = 2 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 88 | 14872 |
| 16 and 50 | 400 |
| 72 and 12 | 72 |
| 92 and 23 | 92 |
| 158 and 163 | 25754 |