
Least Common Multiple (LCM) of 59 and 65
The least common multiple (LCM) of 59 and 65 is 3835.
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 65?
First, calculate the GCD of 59 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 59 ÷ 65 = 0 remainder 59 |
2 | 65 ÷ 59 = 1 remainder 6 |
3 | 59 ÷ 6 = 9 remainder 5 |
4 | 6 ÷ 5 = 1 remainder 1 |
5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
177 and 21 | 1239 |
83 and 171 | 14193 |
39 and 133 | 5187 |
142 and 113 | 16046 |
87 and 22 | 1914 |