Least Common Multiple (LCM) of 59 and 95
The least common multiple (LCM) of 59 and 95 is 5605.
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 59 and 95?
First, calculate the GCD of 59 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 95 = 0 remainder 59 |
| 2 | 95 ÷ 59 = 1 remainder 36 |
| 3 | 59 ÷ 36 = 1 remainder 23 |
| 4 | 36 ÷ 23 = 1 remainder 13 |
| 5 | 23 ÷ 13 = 1 remainder 10 |
| 6 | 13 ÷ 10 = 1 remainder 3 |
| 7 | 10 ÷ 3 = 3 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 191 | 21583 |
| 119 and 135 | 16065 |
| 53 and 105 | 5565 |
| 98 and 49 | 98 |
| 29 and 200 | 5800 |