Least Common Multiple (LCM) of 157 and 68
The least common multiple (LCM) of 157 and 68 is 10676.
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 68?
First, calculate the GCD of 157 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 68 = 2 remainder 21 |
| 2 | 68 ÷ 21 = 3 remainder 5 |
| 3 | 21 ÷ 5 = 4 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 174 | 4524 |
| 131 and 135 | 17685 |
| 110 and 130 | 1430 |
| 11 and 102 | 1122 |
| 27 and 38 | 1026 |