Least Common Multiple (LCM) of 73 and 135
The least common multiple (LCM) of 73 and 135 is 9855.
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 135?
First, calculate the GCD of 73 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 135 = 0 remainder 73 |
| 2 | 135 ÷ 73 = 1 remainder 62 |
| 3 | 73 ÷ 62 = 1 remainder 11 |
| 4 | 62 ÷ 11 = 5 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 85 | 12070 |
| 13 and 184 | 2392 |
| 98 and 86 | 4214 |
| 133 and 105 | 1995 |
| 140 and 14 | 140 |