Least Common Multiple (LCM) of 102 and 157
The least common multiple (LCM) of 102 and 157 is 16014.
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 102 and 157?
First, calculate the GCD of 102 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 157 = 0 remainder 102 |
| 2 | 157 ÷ 102 = 1 remainder 55 |
| 3 | 102 ÷ 55 = 1 remainder 47 |
| 4 | 55 ÷ 47 = 1 remainder 8 |
| 5 | 47 ÷ 8 = 5 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 107 | 15729 |
| 21 and 89 | 1869 |
| 198 and 25 | 4950 |
| 13 and 171 | 2223 |
| 181 and 179 | 32399 |