find the hcf and lcm of 17,102,170
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First, decompise the numbers into their prime factors:
17 is prime, so 17 = 17
To decompose 102:
102 / 2 = 51
51 / 3 = 17
17 is prime, thus 102 = 2 × 3 × 17
To decompose 170:
170 / 2 = 85
85 / 5 = 17
17 is prime, thus 170 = 2 ×5 × 17
Now that they are decomposed the LCM and HCF can simply be found.
The LCM can be found by multiplying together the highest powers of all bases. The bases (primes that the numbers were decomposed into) are all to the power 1, so nothing to worry about there. All the bases we have are: 2, 3, 5 and 17. Therefore, the LCM = 2 × 3 × 5 ×17 = 510.
The HCF can be found by multiplying together the lowest bases of common bases. The only bases that are common between all numbers is 17, therefore the HCF = 17.
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