Least Common Multiple (LCM) of 157 and 51
The least common multiple (LCM) of 157 and 51 is 8007.
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 51?
First, calculate the GCD of 157 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 51 = 3 remainder 4 |
| 2 | 51 ÷ 4 = 12 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 110 | 11330 |
| 171 and 94 | 16074 |
| 186 and 31 | 186 |
| 113 and 101 | 11413 |
| 198 and 114 | 3762 |