Least Common Multiple (LCM) of 142 and 53
The least common multiple (LCM) of 142 and 53 is 7526.
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 142 and 53?
First, calculate the GCD of 142 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 53 = 2 remainder 36 |
| 2 | 53 ÷ 36 = 1 remainder 17 |
| 3 | 36 ÷ 17 = 2 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 83 | 2739 |
| 31 and 139 | 4309 |
| 37 and 131 | 4847 |
| 162 and 14 | 1134 |
| 61 and 14 | 854 |