Least Common Multiple (LCM) of 45 and 147
The least common multiple (LCM) of 45 and 147 is 2205.
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 45 and 147?
First, calculate the GCD of 45 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 147 = 0 remainder 45 |
| 2 | 147 ÷ 45 = 3 remainder 12 |
| 3 | 45 ÷ 12 = 3 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 70 | 840 |
| 112 and 127 | 14224 |
| 83 and 15 | 1245 |
| 69 and 78 | 1794 |
| 169 and 118 | 19942 |