Least Common Multiple (LCM) of 138 and 49
The least common multiple (LCM) of 138 and 49 is 6762.
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 49?
First, calculate the GCD of 138 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 49 = 2 remainder 40 |
| 2 | 49 ÷ 40 = 1 remainder 9 |
| 3 | 40 ÷ 9 = 4 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 76 | 380 |
| 190 and 83 | 15770 |
| 123 and 145 | 17835 |
| 101 and 148 | 14948 |
| 163 and 87 | 14181 |