Least Common Multiple (LCM) of 84 and 157
The least common multiple (LCM) of 84 and 157 is 13188.
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 84 and 157?
First, calculate the GCD of 84 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 157 = 0 remainder 84 |
| 2 | 157 ÷ 84 = 1 remainder 73 |
| 3 | 84 ÷ 73 = 1 remainder 11 |
| 4 | 73 ÷ 11 = 6 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 177 | 22479 |
| 117 and 41 | 4797 |
| 165 and 178 | 29370 |
| 177 and 102 | 6018 |
| 35 and 110 | 770 |