Least Common Multiple (LCM) of 157 and 172
The least common multiple (LCM) of 157 and 172 is 27004.
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 172?
First, calculate the GCD of 157 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 172 = 0 remainder 157 |
| 2 | 172 ÷ 157 = 1 remainder 15 |
| 3 | 157 ÷ 15 = 10 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 186 | 25482 |
| 164 and 193 | 31652 |
| 160 and 77 | 12320 |
| 190 and 46 | 4370 |
| 172 and 85 | 14620 |