Least Common Multiple (LCM) of 73 and 138
The least common multiple (LCM) of 73 and 138 is 10074.
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 73 and 138?
First, calculate the GCD of 73 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 138 = 0 remainder 73 |
| 2 | 138 ÷ 73 = 1 remainder 65 |
| 3 | 73 ÷ 65 = 1 remainder 8 |
| 4 | 65 ÷ 8 = 8 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 45 | 8010 |
| 199 and 71 | 14129 |
| 28 and 190 | 2660 |
| 35 and 64 | 2240 |
| 63 and 132 | 2772 |