Least Common Multiple (LCM) of 133 and 156
The least common multiple (LCM) of 133 and 156 is 20748.
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 156?
First, calculate the GCD of 133 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 156 = 0 remainder 133 |
| 2 | 156 ÷ 133 = 1 remainder 23 |
| 3 | 133 ÷ 23 = 5 remainder 18 |
| 4 | 23 ÷ 18 = 1 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 56 | 840 |
| 117 and 152 | 17784 |
| 28 and 168 | 168 |
| 112 and 113 | 12656 |
| 47 and 166 | 7802 |