Least Common Multiple (LCM) of 157 and 66
The least common multiple (LCM) of 157 and 66 is 10362.
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 66?
First, calculate the GCD of 157 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 66 = 2 remainder 25 |
| 2 | 66 ÷ 25 = 2 remainder 16 |
| 3 | 25 ÷ 16 = 1 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 145 | 2465 |
| 88 and 126 | 5544 |
| 81 and 11 | 891 |
| 148 and 177 | 26196 |
| 137 and 190 | 26030 |