Least Common Multiple (LCM) of 169 and 132
The least common multiple (LCM) of 169 and 132 is 22308.
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 169 and 132?
First, calculate the GCD of 169 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 132 = 1 remainder 37 |
| 2 | 132 ÷ 37 = 3 remainder 21 |
| 3 | 37 ÷ 21 = 1 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 108 | 864 |
| 112 and 169 | 18928 |
| 200 and 59 | 11800 |
| 147 and 160 | 23520 |
| 91 and 11 | 1001 |