Least Common Multiple (LCM) of 49 and 142
The least common multiple (LCM) of 49 and 142 is 6958.
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 49 and 142?
First, calculate the GCD of 49 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 142 = 0 remainder 49 |
| 2 | 142 ÷ 49 = 2 remainder 44 |
| 3 | 49 ÷ 44 = 1 remainder 5 |
| 4 | 44 ÷ 5 = 8 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 120 | 3720 |
| 158 and 75 | 11850 |
| 64 and 162 | 5184 |
| 107 and 88 | 9416 |
| 155 and 88 | 13640 |