Least Common Multiple (LCM) of 138 and 145
The least common multiple (LCM) of 138 and 145 is 20010.
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 145?
First, calculate the GCD of 138 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 145 = 0 remainder 138 |
| 2 | 145 ÷ 138 = 1 remainder 7 |
| 3 | 138 ÷ 7 = 19 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 97 | 2813 |
| 122 and 73 | 8906 |
| 31 and 188 | 5828 |
| 93 and 55 | 5115 |
| 124 and 132 | 4092 |