Common factors /greatest common factors /least common factor

Question

See I am baffling with the concept of above mentioned title I saw one question they wrote find common factors /gcf/lcm of 42,294,882 Please help me out in getting the concept Thanks

Answer 1

Common Factors: All the factors which divides the given numbers. In your case: Common factors are: 2, 3, 7, 21, 42 as these numbers divide all three numbers.

G.C.F. - Greatest Common factor - The greatest number which divides all these numbers. In your case, it is 42.

L.C.M. - Lowest Common Multiple - The number which is divisible by all these numbers

Now as you know: $$ 42 = 2 \times 3 \times 7 $$ $$ 294 = 2 \times 3 \times 7 \times 7 $$ $$ 882 = 2 \times 3 \times 3 \times 7 \times 7 $$

$$ L.C.M. = 2 \times 3 \times 3 \times 7 \times 7 = 882$$