Least Common Multiple (LCM) of 133 and 78
The least common multiple (LCM) of 133 and 78 is 10374.
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 78?
First, calculate the GCD of 133 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 78 = 1 remainder 55 |
| 2 | 78 ÷ 55 = 1 remainder 23 |
| 3 | 55 ÷ 23 = 2 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 23 | 3680 |
| 23 and 106 | 2438 |
| 131 and 51 | 6681 |
| 94 and 117 | 10998 |
| 104 and 125 | 13000 |