Least Common Multiple (LCM) of 157 and 27
The least common multiple (LCM) of 157 and 27 is 4239.
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 27?
First, calculate the GCD of 157 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 27 = 5 remainder 22 |
| 2 | 27 ÷ 22 = 1 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 108 | 1836 |
| 117 and 152 | 17784 |
| 93 and 47 | 4371 |
| 167 and 114 | 19038 |
| 185 and 96 | 17760 |