If three numbers in ratio 3:4:6 have an LCM of 144, how de we find the the GCD and HCF?

Answer 1

Let the numbers be 3x, 4x, and 6x

the LCM of these 3 numbers would be 3*4*x

given : LCM=144

so we can solve for x and find the three numbers

3*4*x= 144

12x=144

x=144/12= 12

the 3 numbers are: 36, 48, and 72

HCF of these three numbers can be found using prime factorization and finding the common factors

Do factor tree for each of the numbers and get the prime factors and write the numbers as product of prime factors:

36 = 2^2 * 3^2

48 = 2^4 * 3

72 = 2^3 * 3^2

from above, we can easily get the common factors for the three numbers

2^2*3 =12

HCF or GCD =12

hope this helps!

Answer 2

144=13x

x=11.0769

33.2, 44.3, 66.46