The hcf of two numbers is 5 and their lcm is 248. if one of the numbers is 10. find the other

Let the ratio be x.

Then, the numbers in the ratio are 3x and 5x.

Now, sum=248-> 3x+5x=248-> 8x=248-> x=248/8

-> x= 31

Now, numbers are-3x=3*31=935x=5*31=155

Last updated - May 05, 2022

Answer: HCF = 4 and LCM = 4960

Step by step solution:

Contents:

Given numbers = 20 and 992

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 20:
20 = 2 × 10
= 2 × 2 × 5

Prime Factorization of 992:

992 = 2 × 496
= 2 × 2 × 248
= 2 × 2 × 2 × 124
= 2 × 2 × 2 × 2 × 62
= 2 × 2 × 2 × 2 × 2 × 31

HCF of 20 and 992 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 2, 2

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

HCF = 2 × 2
= 4

∴ HCF(20, 992) = 4

LCM of 20 and 992 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 2 × 2 × 2 × 2 × 2 × 5 × 31
= 4960

∴ LCM(20, 992) = 4960

Division Method:

HCF of 20 and 992 by division method:

In the above division, the last divisor is 4.

Hence the HCF(GCD) of 20 and 992 = 4

∴ HCF(20, 992) = 4

LCM of 20 and 992 by division method

∴ LCM(20, 992) = 4960

HCF of 20 and 992 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 20:

12451020

Factors of 992:

124816313262124248496992

The greatest common factor in the above lists will be the HCF of the given numbers.

4 is the greatest factor which is common in the above lists.

∴ HCF(20, 992) = 4

If the HCF of two numbers is 4 and their product is 19840, what is their LCM?

Solution:

If the LCM of two numbers is 4960 and their product is 19840, what is their HCF?

Solution:

HCF and LCM of two numbers is 4 and 4960 respectively. If one number is 20, what is the other number?

Solution:

Let other number be x.
Given:
HCF(20, x) = 4
LCM(20, x) = 4960
∵ HCF × LCM = product of numbers
∴ 4 × 4960 = 20 × x
∴ 19840 = 20x
∴ 19840⁄20 = x
∴ x = 992
Hence, the other number is 992.

Solution:

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Last updated - May 03, 2022

Answer: HCF = 2 and LCM = 4956

Step by step solution:

Contents:

Given numbers = 12 and 826

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 12:
12 = 2 × 6
= 2 × 2 × 3

Prime Factorization of 826:

826 = 2 × 413
= 2 × 7 × 59

HCF of 12 and 826 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 2

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

Here, 2 is the only common factor in the above prime factors.

∴ HCF(12, 826) = 2

LCM of 12 and 826 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 2 × 2 × 3 × 7 × 59
= 4956

∴ LCM(12, 826) = 4956

Division Method:

HCF of 12 and 826 by division method:

In the above division, the last divisor is 2.

Hence the HCF(GCF) of 12 and 826 = 2

∴ HCF(12, 826) = 2

LCM of 12 and 826 by division method

∴ LCM(12, 826) = 4956

HCF of 12 and 826 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 12:

1234612

Factors of 826:

1271459118413826

The greatest common factor in the above lists will be the HCF of the given numbers.

2 is the greatest factor which is common in the above lists.

∴ HCF(12, 826) = 2

If the HCF of two numbers is 2 and their product is 9912, what is their LCM?

Solution:

If the LCM of two numbers is 4956 and their product is 9912, what is their HCF?

Solution:

HCF and LCM of two numbers is 2 and 4956 respectively. If one number is 826, what is the other number?

Solution:

Let other number be x.
Given:
HCF(826, x) = 2
LCM(826, x) = 4956
∵ HCF × LCM = product of numbers
∴ 2 × 4956 = 826 × x
∴ 9912 = 826x
∴ 9912⁄826 = x
∴ x = 12
Hence, the other number is 12.