Integers question Mathematics 4024. . . .

[ailg1996]

Calculators not allowed / . . . .its a paper 1 question

Written as the product of its prime factors, 360 = 23 × 32 × 5.
(a) Write 108 as the product of its prime factors.
(b) Find the lowest common multiple of 108 and 360.
Give your answer as the product of its prime factors.
(c) Find the smallest positive integer k such that 360 k is a cube number.

 

[Nibz]

The first part is simple => It would be 2 * 2 into 3*3*3!
for (b) the L.C.M of both those number is = 1080
Prime Factors of 1080:
1080 = 2 * 540
540 = 2 * 270
270 = 2 * 135
135 = 3 * 45
45 = 3 * 15
15 = 3 * 5
5 = 5 * 1
=> 2*2*2 into 3*3*3 into 5

for (c) it is 3 x 5^2 = 75

Kindly check these answers with the book ones.

 

[abcde]

AOA!
(a) Factorise 108. you'll get 108 = 2^2 x 3^3
(b) L.C.M. = 2^3 x 3^3 x 5
(c) k = 3 x 5^2 = 3 x 25 = 75.