
Least Common Multiple (LCM) of 45 and 59
The least common multiple (LCM) of 45 and 59 is 2655.
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 45 and 59?
First, calculate the GCD of 45 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 45 ÷ 59 = 0 remainder 45 |
2 | 59 ÷ 45 = 1 remainder 14 |
3 | 45 ÷ 14 = 3 remainder 3 |
4 | 14 ÷ 3 = 4 remainder 2 |
5 | 3 ÷ 2 = 1 remainder 1 |
6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
110 and 81 | 8910 |
195 and 146 | 28470 |
60 and 122 | 3660 |
140 and 56 | 280 |
16 and 74 | 592 |