
Least Common Multiple (LCM) of 45 and 144
The least common multiple (LCM) of 45 and 144 is 720.
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 144?
First, calculate the GCD of 45 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 45 ÷ 144 = 0 remainder 45 |
2 | 144 ÷ 45 = 3 remainder 9 |
3 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
98 and 132 | 6468 |
150 and 14 | 1050 |
156 and 90 | 2340 |
128 and 144 | 1152 |
188 and 195 | 36660 |