Least Common Multiple (LCM) of 45 and 63
The least common multiple (LCM) of 45 and 63 is 315.
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 63?
First, calculate the GCD of 45 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 63 = 0 remainder 45 |
| 2 | 63 ÷ 45 = 1 remainder 18 |
| 3 | 45 ÷ 18 = 2 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 123 | 7257 |
| 19 and 29 | 551 |
| 173 and 78 | 13494 |
| 115 and 16 | 1840 |
| 108 and 175 | 18900 |