Least Common Multiple (LCM) of 21 and 140
The least common multiple (LCM) of 21 and 140 is 420.
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 21 and 140?
First, calculate the GCD of 21 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 140 = 0 remainder 21 |
| 2 | 140 ÷ 21 = 6 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 175 | 29050 |
| 29 and 44 | 1276 |
| 68 and 27 | 1836 |
| 127 and 41 | 5207 |
| 113 and 87 | 9831 |