Least Common Multiple (LCM) of 101 and 53
The least common multiple (LCM) of 101 and 53 is 5353.
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 101 and 53?
First, calculate the GCD of 101 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 53 = 1 remainder 48 |
| 2 | 53 ÷ 48 = 1 remainder 5 |
| 3 | 48 ÷ 5 = 9 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 23 | 1150 |
| 114 and 35 | 3990 |
| 168 and 49 | 1176 |
| 70 and 182 | 910 |
| 120 and 77 | 9240 |