Least Common Multiple (LCM) of 58 and 132
The least common multiple (LCM) of 58 and 132 is 3828.
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 58 and 132?
First, calculate the GCD of 58 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 132 = 0 remainder 58 |
| 2 | 132 ÷ 58 = 2 remainder 16 |
| 3 | 58 ÷ 16 = 3 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 136 | 15368 |
| 188 and 147 | 27636 |
| 47 and 144 | 6768 |
| 172 and 83 | 14276 |
| 157 and 101 | 15857 |