Least Common Multiple (LCM) of 75 and 55
The least common multiple (LCM) of 75 and 55 is 825.
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 55?
First, calculate the GCD of 75 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 55 = 1 remainder 20 |
| 2 | 55 ÷ 20 = 2 remainder 15 |
| 3 | 20 ÷ 15 = 1 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 72 | 936 |
| 157 and 141 | 22137 |
| 160 and 195 | 6240 |
| 149 and 24 | 3576 |
| 99 and 70 | 6930 |