Least Common Multiple (LCM) of 53 and 73
The least common multiple (LCM) of 53 and 73 is 3869.
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 53 and 73?
First, calculate the GCD of 53 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 73 = 0 remainder 53 |
| 2 | 73 ÷ 53 = 1 remainder 20 |
| 3 | 53 ÷ 20 = 2 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 77 | 8855 |
| 126 and 70 | 630 |
| 41 and 178 | 7298 |
| 81 and 28 | 2268 |
| 160 and 197 | 31520 |