Least Common Multiple (LCM) of 75 and 148
The least common multiple (LCM) of 75 and 148 is 11100.
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 75 and 148?
First, calculate the GCD of 75 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 148 = 0 remainder 75 |
| 2 | 148 ÷ 75 = 1 remainder 73 |
| 3 | 75 ÷ 73 = 1 remainder 2 |
| 4 | 73 ÷ 2 = 36 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 80 | 7920 |
| 15 and 60 | 60 |
| 96 and 138 | 2208 |
| 63 and 60 | 1260 |
| 93 and 117 | 3627 |