Least Common Multiple (LCM) of 51 and 147
The least common multiple (LCM) of 51 and 147 is 2499.
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 51 and 147?
First, calculate the GCD of 51 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 147 = 0 remainder 51 |
| 2 | 147 ÷ 51 = 2 remainder 45 |
| 3 | 51 ÷ 45 = 1 remainder 6 |
| 4 | 45 ÷ 6 = 7 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 165 | 20130 |
| 132 and 33 | 132 |
| 47 and 126 | 5922 |
| 129 and 65 | 8385 |
| 140 and 46 | 3220 |