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Answer 1 · 2017-08-31T16:31:36

$70$ $70$

The Least Common Denominator (L.C.D) as you said, can be gotten from the Lowest Common Multiple (L.C.M) from of the two digits..

Hence we have for $10 = 2 \times 5$ $10 = 2 xx 5$ and $14 = 2 \times 7$ $14 = 2 xx 7$

Since $2$ $2$ is both common between them, we should take of of the $2's$ instead of both..

Hence the L.C.M for both digits are $-> 2 xx 5 xx 7 = 70$

Hence the L.C.D of $10$ and $14$ is $70$

Though the L.C.D, is best explained using fractions, but what is given is just whole number..

To make it more crystal..

An example, Find the L.C.D of $1/2 + 1/4 = ?$

Like i said it has to do with the Denominators, like making the denominators common..

$1/color(blue)2 + 1/color(blue)4$

We have $2 and 4$ as the respective denominators, so in other to make it common, we have to look for the L.C.M

L.C.M of $2 = color(red)2$

L.C.M of $4 = color(red)2 xx 2$

The one in red color is common in both digits, so we will just take one $2$ out of them both..

$:.$ L.C.M of $2 and 4 = color(red)2 xx 2 = 4$

$rArr L.C.D = 4$

$rArr 1/4 + 1/4$

Hope this helps!