Least Common Multiple (LCM) of 45 and 72
The least common multiple (LCM) of 45 and 72 is 360.
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 72?
First, calculate the GCD of 45 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 72 = 0 remainder 45 |
| 2 | 72 ÷ 45 = 1 remainder 27 |
| 3 | 45 ÷ 27 = 1 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 44 | 2596 |
| 109 and 105 | 11445 |
| 29 and 67 | 1943 |
| 167 and 145 | 24215 |
| 91 and 186 | 16926 |