Least Common Multiple (LCM) of 45 and 26
The least common multiple (LCM) of 45 and 26 is 1170.
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 26?
First, calculate the GCD of 45 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 26 = 1 remainder 19 |
| 2 | 26 ÷ 19 = 1 remainder 7 |
| 3 | 19 ÷ 7 = 2 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 88 | 4136 |
| 175 and 99 | 17325 |
| 123 and 17 | 2091 |
| 65 and 157 | 10205 |
| 90 and 61 | 5490 |