Least Common Multiple (LCM) of 133 and 162
The least common multiple (LCM) of 133 and 162 is 21546.
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 162?
First, calculate the GCD of 133 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 162 = 0 remainder 133 |
| 2 | 162 ÷ 133 = 1 remainder 29 |
| 3 | 133 ÷ 29 = 4 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 154 | 924 |
| 15 and 53 | 795 |
| 70 and 116 | 4060 |
| 63 and 100 | 6300 |
| 160 and 95 | 3040 |