Least Common Multiple (LCM) of 45 and 101
The least common multiple (LCM) of 45 and 101 is 4545.
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 101?
First, calculate the GCD of 45 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 101 = 0 remainder 45 |
| 2 | 101 ÷ 45 = 2 remainder 11 |
| 3 | 45 ÷ 11 = 4 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 120 | 600 |
| 123 and 77 | 9471 |
| 106 and 64 | 3392 |
| 195 and 179 | 34905 |
| 30 and 148 | 2220 |