Least Common Multiple (LCM) of 132 and 169
The least common multiple (LCM) of 132 and 169 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 132 and 169?
First, calculate the GCD of 132 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 169 = 0 remainder 132 |
| 2 | 169 ÷ 132 = 1 remainder 37 |
| 3 | 132 ÷ 37 = 3 remainder 21 |
| 4 | 37 ÷ 21 = 1 remainder 16 |
| 5 | 21 ÷ 16 = 1 remainder 5 |
| 6 | 16 ÷ 5 = 3 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 19 | 2394 |
| 88 and 44 | 88 |
| 132 and 144 | 1584 |
| 88 and 141 | 12408 |
| 194 and 111 | 21534 |