Least Common Multiple (LCM) of 75 and 43
The least common multiple (LCM) of 75 and 43 is 3225.
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 43?
First, calculate the GCD of 75 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 43 = 1 remainder 32 |
| 2 | 43 ÷ 32 = 1 remainder 11 |
| 3 | 32 ÷ 11 = 2 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 142 | 25702 |
| 55 and 164 | 9020 |
| 10 and 31 | 310 |
| 149 and 88 | 13112 |
| 148 and 155 | 22940 |