hcf and lcm 120 and 288
using primefactorization
Answers
Answer:
In some questions the highest common factor (HCF) or lowest common multiple (LCM) of two large numbers may need to be found.
It would take a long time to write out all the factors and multiples of 24 and 180 and compare the lists and it would be easy to make a mistake.
A more efficient method is to use prime factors.
Using prime factors to find the HCF and LCM
Numbers can be broken down into prime factors using prime factor trees. When the prime factors of two numbers are known, they can be compared to calculate HCFs and LCMs. This can be a more efficient method than listing the factors and multiples of large numbers.
Example
Find the HCF and LCM of 24 and 180.
Start by writing 24 and 180 as the product of their prime factors.
Factor trees of 24 and 180
The product of prime factors for 24 is: 2 \times 2 \times 2 \times 3
The product of prime factors for 180 is: 2 \times 2 \times 3 \times 3 \times 5
To find the HCF, find any prime factors that are in common between the products. Each product contains two 2s and one 3, so use these for the HCF.
HCF = 2 \times 2 \times 3 = 12
Cross any numbers used so far off from the products.
The product of prime factors for 24 is: \cancel2\times\cancel2\times2\times\cancel3
The product of prime factors for 180 is: \cancel2\times\cancel2\times\cancel3\times3\times5
To find the LCM, multiply the HCF by all the numbers in the products that have not yet been used.
LCM = 12 \times 2 \times 3 \times 5 = 360
Answer:
HCF = 24
LCM = 1440
Step-by-step explanation:
120 = 2 × 2 × 2 × 3 × 5
288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
HCF of 120 and 288 is 2 × 2 × 2 × 3 = 24
LCM of 120 and 288 is
2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440
hope you get your answer