Least Common Multiple (LCM) of 157 and 84
The least common multiple (LCM) of 157 and 84 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 157 and 84?
First, calculate the GCD of 157 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 84 = 1 remainder 73 |
| 2 | 84 ÷ 73 = 1 remainder 11 |
| 3 | 73 ÷ 11 = 6 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 96 | 13920 |
| 52 and 100 | 1300 |
| 98 and 56 | 392 |
| 76 and 105 | 7980 |
| 12 and 50 | 300 |