find the LCM and HCF of the given number 96 and 120
Answers
Answer:
Steps to find LCM
Find the prime factorization of 96
96 = 2 × 2 × 2 × 2 × 2 × 3
Find the prime factorization of 120
120 = 2 × 2 × 2 × 3 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 5
LCM = 480
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Step-by-step explanation:
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Answer:
LCM=480 HCF=24
Step-by-step explanation:
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List all prime factors for each number.
Prime Factorization of 96 is:
2 x 2 x 2 x 2 x 2 x 3 => 25 x 31
Prime Factorization of 120 is:
2 x 2 x 2 x 3 x 5 => 23 x 31 x 51
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Then the greatest common factor is 24.
The new superset list is
2, 2, 2, 2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 5 = 480
In exponential form:
LCM = 25 x 31 x 51 = 480
LCM = 480
Therefore,
LCM(96, 120) = 480