Least Common Multiple (LCM) of 157 and 164
The least common multiple (LCM) of 157 and 164 is 25748.
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 164?
First, calculate the GCD of 157 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 164 = 0 remainder 157 |
| 2 | 164 ÷ 157 = 1 remainder 7 |
| 3 | 157 ÷ 7 = 22 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 53 | 5300 |
| 75 and 119 | 8925 |
| 152 and 135 | 20520 |
| 50 and 184 | 4600 |
| 194 and 179 | 34726 |