Least Common Multiple (LCM) of 53 and 90
The least common multiple (LCM) of 53 and 90 is 4770.
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 53 and 90?
First, calculate the GCD of 53 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 90 = 0 remainder 53 |
| 2 | 90 ÷ 53 = 1 remainder 37 |
| 3 | 53 ÷ 37 = 1 remainder 16 |
| 4 | 37 ÷ 16 = 2 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 134 | 7370 |
| 193 and 127 | 24511 |
| 142 and 117 | 16614 |
| 18 and 32 | 288 |
| 102 and 54 | 918 |