# Find the HCF anb LCM of the number given below .verify that their product is equal to the product of the given number. i?32,37 ii?46,51 iii?15,60 iv?18,63 V?78,104.

Dear Student

1 - 32, 37
LCM
By Prime Factors
List all prime factors of each denominator, and find the union of these primes
prime Factors of 32
: 2, 2, 2, 2, 2
Prime Factors of 37
: 37
Therefore, the LCM is $2\times 2\times 2\times 2\times 2\times 37=1184$.

HCF
By Prime Factors
List all prime factors of each denominator, and find the intersection of these primes.
Prime Factors of 32
: 2, 2, 2, 2, 2
Prime Factors of 37
: 37
There is no prime factor shared by all numbers. Therefore, the HCF is $1$.

=>32*37=1184

=lcm*Hcf=1184*1=1184
hence LCM *HCF=product of the numbers

Q-2
46,51
LCM
By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
Prime Factors of 46
: 2, 23
Prime Factors of 51
: 3, 17
Therefore, the LCM is $2\times 3\times 17\times 23=2346$.
HCF
By Prime Factors
List all prime factors of each denominator, and find the intersection of these primes.
Prime Factors of 46
: 2, 23
Prime Factors of 51
: 3, 17
There is no prime factor shared by all numbers. Therefore, the HCF is $1$.

=>46*51=2346
=>LCM * HCF=2346*1=2346
HENCE  LCM *HCF=product of the numbers

Q-3
15,60
LCM
By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
Prime Factors of 15
: 3, 5
Prime Factors of 60
: 2, 2, 3, 5
Therefore, the LCM is $2\times 2\times 3\times 5=60$.

HCF
2: By Prime Factors
List all prime factors of each denominator, and find the intersection of these primes.
Prime Factors of 15
: 3, 5
Prime Factors of 60
: 2, 2, 3, 5
Therefore, the HCF is $3\times 5=15$.

=>15*60=900
=>LCM*HCF=60*15=900
HENCE  LCM *HCF=product of the numbers

Q-4
18,63
LCM
By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
Prime Factors of 18
: 2, 3, 3
Prime Factors of 63
: 3, 3, 7
Therefore, the LCM is $2\times 3\times 3\times 7=126$.

HCF
By Prime Factors
List all prime factors of each denominator, and find the intersection of these primes.
Prime Factors of 18
: 2, 3, 3
Prime Factors of 63
: 3, 3, 7
Therefore, the HCF is $3\times 3=9$.

=>18*63=1134
=>LCM*HCF=126*9=1134
HENCE  LCM *HCF=product of the numbers

Q-5
78,104
LCM
By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
Prime Factors of 78
: 2, 3, 13
Prime Factors of 104
: 2, 2, 2, 13
Therefore, the LCM is $2\times 2\times 2\times 3\times 13=312$.

HCF
By Prime Factors
List all prime factors of each denominator, and find the intersection of these primes.
Prime Factors of 78
: 2, 3, 13
Prime Factors of 104
: 2, 2, 2, 13
Therefore, the HCF is $2\times 13=26$.
=>78*104=8112
=>LCM*HCF=312*26=8112
HENCE  LCM *HCF=product of the numbers

regards

• -2
What are you looking for?