Least Common Multiple (LCM) of 35 and 144
The least common multiple (LCM) of 35 and 144 is 5040.
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 35 and 144?
First, calculate the GCD of 35 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 144 = 0 remainder 35 |
| 2 | 144 ÷ 35 = 4 remainder 4 |
| 3 | 35 ÷ 4 = 8 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 114 | 9690 |
| 173 and 114 | 19722 |
| 149 and 165 | 24585 |
| 117 and 72 | 936 |
| 160 and 197 | 31520 |