Least Common Multiple (LCM) of 133 and 72
The least common multiple (LCM) of 133 and 72 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 133 and 72?
First, calculate the GCD of 133 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 72 = 1 remainder 61 |
| 2 | 72 ÷ 61 = 1 remainder 11 |
| 3 | 61 ÷ 11 = 5 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 120 | 1320 |
| 45 and 179 | 8055 |
| 66 and 131 | 8646 |
| 153 and 153 | 153 |
| 198 and 163 | 32274 |