Least Common Multiple (LCM) of 105 and 72
The least common multiple (LCM) of 105 and 72 is 2520.
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 105 and 72?
First, calculate the GCD of 105 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 72 = 1 remainder 33 |
| 2 | 72 ÷ 33 = 2 remainder 6 |
| 3 | 33 ÷ 6 = 5 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 38 | 6422 |
| 65 and 41 | 2665 |
| 146 and 169 | 24674 |
| 129 and 194 | 25026 |
| 10 and 22 | 110 |