Least Common Multiple (LCM) of 74 and 132
The least common multiple (LCM) of 74 and 132 is 4884.
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 74 and 132?
First, calculate the GCD of 74 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 132 = 0 remainder 74 |
| 2 | 132 ÷ 74 = 1 remainder 58 |
| 3 | 74 ÷ 58 = 1 remainder 16 |
| 4 | 58 ÷ 16 = 3 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 43 | 4515 |
| 166 and 87 | 14442 |
| 120 and 107 | 12840 |
| 45 and 108 | 540 |
| 80 and 39 | 3120 |