Least Common Multiple (LCM) of 48 and 76
The least common multiple (LCM) of 48 and 76 is 912.
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 48 and 76?
First, calculate the GCD of 48 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 76 = 0 remainder 48 |
| 2 | 76 ÷ 48 = 1 remainder 28 |
| 3 | 48 ÷ 28 = 1 remainder 20 |
| 4 | 28 ÷ 20 = 1 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 64 | 10560 |
| 165 and 57 | 3135 |
| 179 and 32 | 5728 |
| 146 and 84 | 6132 |
| 132 and 69 | 3036 |