Least Common Multiple (LCM) of 156 and 133
The least common multiple (LCM) of 156 and 133 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 156 and 133?
First, calculate the GCD of 156 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 133 = 1 remainder 23 |
| 2 | 133 ÷ 23 = 5 remainder 18 |
| 3 | 23 ÷ 18 = 1 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 130 | 2080 |
| 114 and 63 | 2394 |
| 129 and 35 | 4515 |
| 133 and 136 | 18088 |
| 17 and 144 | 2448 |