Least Common Multiple (LCM) of 157 and 169
The least common multiple (LCM) of 157 and 169 is 26533.
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 169?
First, calculate the GCD of 157 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 169 = 0 remainder 157 |
| 2 | 169 ÷ 157 = 1 remainder 12 |
| 3 | 157 ÷ 12 = 13 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 188 | 10716 |
| 84 and 176 | 3696 |
| 185 and 17 | 3145 |
| 120 and 171 | 6840 |
| 96 and 45 | 1440 |