Least Common Multiple (LCM) of 109 and 132
The least common multiple (LCM) of 109 and 132 is 14388.
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 109 and 132?
First, calculate the GCD of 109 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 132 = 0 remainder 109 |
| 2 | 132 ÷ 109 = 1 remainder 23 |
| 3 | 109 ÷ 23 = 4 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 87 | 1914 |
| 28 and 110 | 1540 |
| 101 and 107 | 10807 |
| 73 and 137 | 10001 |
| 44 and 105 | 4620 |