Find the h.c.f, if the numbers are in the ratio of 4 : 5 : 6 and their l.c.m. is 2400
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By taking out x common we get 4x 5x 6x
since their LCM is 2400 thus their sum must be equal to their LCM
thus 4x+5x+6x = 2400
15x = 2400
x = 2400/15
thus x equals to 160
so putting x into 4x 5x 6x
4 *160=640
5*160=800
6*160=960
Now by taking their HCF we get
5*2*2*2*2*2*2*2*3*5
which results in 9600
thus their HCF is 9600
since their LCM is 2400 thus their sum must be equal to their LCM
thus 4x+5x+6x = 2400
15x = 2400
x = 2400/15
thus x equals to 160
so putting x into 4x 5x 6x
4 *160=640
5*160=800
6*160=960
Now by taking their HCF we get
5*2*2*2*2*2*2*2*3*5
which results in 9600
thus their HCF is 9600
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