Least Common Multiple (LCM) of 63 and 75
The least common multiple (LCM) of 63 and 75 is 1575.
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 63 and 75?
First, calculate the GCD of 63 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 75 = 0 remainder 63 |
| 2 | 75 ÷ 63 = 1 remainder 12 |
| 3 | 63 ÷ 12 = 5 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 96 | 7008 |
| 89 and 14 | 1246 |
| 160 and 112 | 1120 |
| 116 and 55 | 6380 |
| 192 and 156 | 2496 |