Least Common Multiple (LCM) of 47 and 36
The least common multiple (LCM) of 47 and 36 is 1692.
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 47 and 36?
First, calculate the GCD of 47 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 36 = 1 remainder 11 |
| 2 | 36 ÷ 11 = 3 remainder 3 |
| 3 | 11 ÷ 3 = 3 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 135 | 24030 |
| 12 and 131 | 1572 |
| 91 and 12 | 1092 |
| 57 and 32 | 1824 |
| 172 and 78 | 6708 |