Least Common Multiple (LCM) of 138 and 157
The least common multiple (LCM) of 138 and 157 is 21666.
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 138 and 157?
First, calculate the GCD of 138 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 157 = 0 remainder 138 |
| 2 | 157 ÷ 138 = 1 remainder 19 |
| 3 | 138 ÷ 19 = 7 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 146 | 3358 |
| 145 and 104 | 15080 |
| 103 and 138 | 14214 |
| 33 and 141 | 1551 |
| 146 and 99 | 14454 |