Least Common Multiple (LCM) of 34 and 132
The least common multiple (LCM) of 34 and 132 is 2244.
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 34 and 132?
First, calculate the GCD of 34 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 132 = 0 remainder 34 |
| 2 | 132 ÷ 34 = 3 remainder 30 |
| 3 | 34 ÷ 30 = 1 remainder 4 |
| 4 | 30 ÷ 4 = 7 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 25 | 3450 |
| 169 and 77 | 13013 |
| 79 and 18 | 1422 |
| 27 and 13 | 351 |
| 130 and 196 | 12740 |