Least Common Multiple (LCM) of 90 and 143
The least common multiple (LCM) of 90 and 143 is 12870.
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 90 and 143?
First, calculate the GCD of 90 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 143 = 0 remainder 90 |
| 2 | 143 ÷ 90 = 1 remainder 53 |
| 3 | 90 ÷ 53 = 1 remainder 37 |
| 4 | 53 ÷ 37 = 1 remainder 16 |
| 5 | 37 ÷ 16 = 2 remainder 5 |
| 6 | 16 ÷ 5 = 3 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 14 | 770 |
| 16 and 104 | 208 |
| 147 and 64 | 9408 |
| 55 and 161 | 8855 |
| 126 and 170 | 10710 |