Question 1408: what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112? i'm too tired to try this anymore!
Thanks!
Found 2 solutions by AnlytcPhil, tanny:
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112? i'm too tired to
try this anymore! Thanks!
It's asking "What is the smallest integer that 82,96 and 112 will divide into evenly?
Prime factor 82:
82 = 2·41
Prime factor 96
96 = 2·48 = 2·2·24 = 2·2·2·12 = 2·2·2·2·6 = 2·2·2·2·2·3
Prime factor 112
96 = 2·56 = 2·2·28 = 2·2·2·14 = 2·2·2·2·7
So we have
82 = 2·41
96 = 2·2·2·2·2·3
112 = 2·2·2·2·7
82 contains 2 ONE time, 96 contains 2 FIVE times, 112 contains 2 FOUR times.
The largest of ONE, FIVE and FOUR is FIVE, so the LCM must contain 2 FIVE times.
82 contains 41 ONE time, 96 contains 41 ZERO times, 112 contains 41 ZERO
times. The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 41
ONE time.
96 contains 3 ONE time, 82 contains 3 ZERO times, 112 contains 3 ZERO times.
The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 3 ONE time.
112 contains 7 ONE time, 82 contains 7 ZERO times, 96 contains 7 ONE times.
The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 7 ONE time.
So the LCM is the integer that contains 2 FIVE times, 41 ONE time, 3 ONE time,
and 7 ONE time is 2·2·2·2·2·41·3·7 = 27552
Edwin
Answer by tanny(2)  (Show Source):
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