Least Common Multiple (LCM) of 45 and 153
The least common multiple (LCM) of 45 and 153 is 765.
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 153?
First, calculate the GCD of 45 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 153 = 0 remainder 45 |
| 2 | 153 ÷ 45 = 3 remainder 18 |
| 3 | 45 ÷ 18 = 2 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 111 | 13542 |
| 21 and 84 | 84 |
| 150 and 82 | 6150 |
| 95 and 154 | 14630 |
| 68 and 76 | 1292 |