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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
 

 

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