Least Common Multiple (LCM) of 60 and 95
The least common multiple (LCM) of 60 and 95 is 1140.
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 60 and 95?
First, calculate the GCD of 60 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 95 = 0 remainder 60 |
| 2 | 95 ÷ 60 = 1 remainder 35 |
| 3 | 60 ÷ 35 = 1 remainder 25 |
| 4 | 35 ÷ 25 = 1 remainder 10 |
| 5 | 25 ÷ 10 = 2 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 166 | 21414 |
| 14 and 100 | 700 |
| 132 and 107 | 14124 |
| 42 and 176 | 3696 |
| 63 and 110 | 6930 |