Least Common Multiple (LCM) of 157 and 88
The least common multiple (LCM) of 157 and 88 is 13816.
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 88?
First, calculate the GCD of 157 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 88 = 1 remainder 69 |
| 2 | 88 ÷ 69 = 1 remainder 19 |
| 3 | 69 ÷ 19 = 3 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 165 | 1980 |
| 123 and 180 | 7380 |
| 148 and 69 | 10212 |
| 52 and 152 | 1976 |
| 182 and 184 | 16744 |