Least Common Multiple (LCM) of 72 and 133
The least common multiple (LCM) of 72 and 133 is 9576.
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 72 and 133?
First, calculate the GCD of 72 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 133 = 0 remainder 72 |
| 2 | 133 ÷ 72 = 1 remainder 61 |
| 3 | 72 ÷ 61 = 1 remainder 11 |
| 4 | 61 ÷ 11 = 5 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 79 | 14062 |
| 169 and 36 | 6084 |
| 184 and 14 | 1288 |
| 174 and 198 | 5742 |
| 133 and 13 | 1729 |