Question

the numbers 176 and 342, written as the products of their prime factors, are 176 = 2 to the power of 4 x 11 and 342 = 2 x 3 square x 19. Hence, Find the smallest whole number that is divisible by both 176 and 342

Answer 1

Step-by-step explanation:

find the least common multiple. start by factoring both nos.

176=>

16×11=>

2^4×11

342=>

3×114

3×3×38

2×3^2×19

2^4×3^2×11×19 would be the least common multiple. note what I did. I looked at all the factors for each no. and selected the highest power of each one.

16×9×11×19

16×9×209

(16×209)×9

16×(200+9)×9

(16×200+16×9)×9

(3200+144)×9

3344×9

9×(3000+300+40+4)

27000+2700+360+36

29700+396

30096.