Least Common Multiple (LCM) of 55 and 95
The least common multiple (LCM) of 55 and 95 is 1045.
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 55 and 95?
First, calculate the GCD of 55 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 95 = 0 remainder 55 |
| 2 | 95 ÷ 55 = 1 remainder 40 |
| 3 | 55 ÷ 40 = 1 remainder 15 |
| 4 | 40 ÷ 15 = 2 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 157 | 27318 |
| 157 and 61 | 9577 |
| 20 and 19 | 380 |
| 100 and 27 | 2700 |
| 141 and 163 | 22983 |