Least Common Multiple (LCM) of 45 and 53
The least common multiple (LCM) of 45 and 53 is 2385.
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 45 and 53?
First, calculate the GCD of 45 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 53 = 0 remainder 45 |
| 2 | 53 ÷ 45 = 1 remainder 8 |
| 3 | 45 ÷ 8 = 5 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 83 | 11454 |
| 194 and 83 | 16102 |
| 99 and 167 | 16533 |
| 141 and 119 | 16779 |
| 119 and 137 | 16303 |