Question

6. given three numbers 12, 40 and 45, find... a) their HCF b) their LCM b) the greatest 4-digit number which is a common multiple of these numbers.

Answer 1

Answer:

a) HCF = Highest common factor

Factors of :-

12:- 1,2,3,4,6,12

40:- 1,2,4,5,8,10,20,40

45:- 1,3,5,9,15,45

HCF = 1 (nothing else is common)

b) LCM= Lowest Common Multiple

Multiples of :-

12:- 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360

40:- 40, 80, 120, 160, 200, 240, 280, 320, 360, 400

45:- 45, 90, 135, 180, 225, 270, 315, 360, 405, 450

In all 360 is the least common

so..

LCM=360

c)the greatest 4-digit number which is a common multiple of these numbers.

First find the LCM.. Find the attached file....

LCM = 3x3x2x2x2x5

        = 360

now form pairs

3x2 (2 &5 dont have)

s0..

lcm x (5x2)

= 360x10

= 3600 ( greatest 4 digit number)