The product of HCF and LCM of two numbers is 119. Find the two numbers if one of the numbers is not 1. Please help me to solve this.
Did you notice that
119 = 7 x 17 , that is, its only factors are prime numbers.
If we needed the HCF of
7 and 17 it would be 1
If we needed the LCM of
7 and 17 it would be 119
The product of 1 and 119 is 119
Our two numbers are 7 and 17
Further investigation:
suppose we have two numbers that have a common factor, e.g. 15 and 24
15 = 3x5
24 = 3x2x2x2
so LCF = 3
HCM = 3x5x8 = 120
product of 3 and 120 = 360
360 = 3x3x5x8 = 3^2 (5x8) which splits into 3x5 and 3x8
notice we have the square of the common factor times the other non-common factors
so our 119 = 1^2 (7x17)
which splits into 1x7 and 1x17
consider a product such as
5^2 (9x7) or 1575 as the product of the HCF and LCM
What were the two numbers?
According to the above, they would have been
5x9 and 5x7 or 45 and 35
check
for 45 and 35 , the HCF is 5
and the LCM = 5x9x7 or 315
then the product of the LCF and the HCM
is 5x315 = 1575
YeaHHHHH!
Excellent. Thanks
do you notice that 119=into 17, that os its only factors are prime numbers.If we needed the HCF of 7 and 17 it would be 1.If we need the LCM of 7 and 17 it would be 119.The product of 1 and 119 is 119 is 119.our two numbers are 7 and 17.
the product of hcf and lcm is 119 find the two numbers if none of them is one
I want same answer
To solve this problem, let's break it down step by step:
Step 1: Let's assume the two numbers are x and y, where x is not equal to 1.
Step 2: We need to find the HCF (highest common factor) and LCM (lowest common multiple) of x and y.
Step 3: The product of the HCF and LCM is given as 119. So, we can write the equation as:
HCF(x, y) * LCM(x, y) = 119
Step 4: Now, we need to find the prime factors of 119. Prime factors of 119 are 7 and 17.
Step 5: Let's consider the possibilities for the HCF and LCM:
a) HCF(x, y) = 1 and LCM(x, y) = 119
In this case, the two numbers would be 1 and 119, which goes against the condition given in the problem.
b) HCF(x, y) = 7 and LCM(x, y) = 17
In this case, the two numbers would be 7 and 17, which satisfies the condition that one of the numbers is not 1.
So, the two numbers are 7 and 17.
To summarize:
The two numbers are 7 and 17, with the HCF being 7 and the LCM being 17.