50 as a product of its prime factors is 5*5*2
70 as a product of its prime factors is 5*7*2
For the lowest common multiple you must include all the prime factors but if they are in both products then you only need to include it once.
SO lowest common multiple is 5*5*2*7 = 350
LCM 50 and 70
Let us see:
50=2 x 5 x 5
70=2 x5 x 7
So we take 2 x 5 x 5 x 7=350
Because we have a pair of 2's, we take only one
And because 50 has a pair of 5's we take only one
And so we are left with 2 x 5 x 5 x7=350 I think!!!!!!!. It was a century ago when I did this!