Least Common Multiple (LCM) of 157 and 174
The least common multiple (LCM) of 157 and 174 is 27318.
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 174?
First, calculate the GCD of 157 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 174 = 0 remainder 157 |
| 2 | 174 ÷ 157 = 1 remainder 17 |
| 3 | 157 ÷ 17 = 9 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 114 | 4674 |
| 195 and 110 | 4290 |
| 184 and 138 | 552 |
| 58 and 180 | 5220 |
| 22 and 96 | 1056 |