Least Common Multiple (LCM) of 157 and 102
The least common multiple (LCM) of 157 and 102 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 157 and 102?
First, calculate the GCD of 157 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 102 = 1 remainder 55 |
| 2 | 102 ÷ 55 = 1 remainder 47 |
| 3 | 55 ÷ 47 = 1 remainder 8 |
| 4 | 47 ÷ 8 = 5 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 39 | 4875 |
| 111 and 64 | 7104 |
| 189 and 19 | 3591 |
| 24 and 32 | 96 |
| 145 and 120 | 3480 |