Least Common Multiple (LCM) of 157 and 19
The least common multiple (LCM) of 157 and 19 is 2983.
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 19?
First, calculate the GCD of 157 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 19 = 8 remainder 5 |
| 2 | 19 ÷ 5 = 3 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 99 | 1980 |
| 15 and 73 | 1095 |
| 167 and 93 | 15531 |
| 27 and 108 | 108 |
| 172 and 200 | 8600 |