Least Common Multiple (LCM) of 53 and 97
The least common multiple (LCM) of 53 and 97 is 5141.
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 97?
First, calculate the GCD of 53 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 97 = 0 remainder 53 |
| 2 | 97 ÷ 53 = 1 remainder 44 |
| 3 | 53 ÷ 44 = 1 remainder 9 |
| 4 | 44 ÷ 9 = 4 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 115 | 11040 |
| 116 and 134 | 7772 |
| 126 and 170 | 10710 |
| 100 and 57 | 5700 |
| 180 and 114 | 3420 |