Tuesday, January 19, 2016
[S1_Expository] Exploring the HCF and LCM with a calculator
How does it work?
When we reduce a fraction to its lowest terms, we actually cancel out as many common factors as possible. So eventually the numerator and the denominator of original fraction get cancelled by their Highest Common Factor (HCF), a.k.a. “Greatest Common Divisor (GCD) ” in
. Just as America England
are divided by a common language(*), we can divide 756
by 6 to get the HCF. Why?
That is because 756 was divided by the HCF to get 6. You
may try a similar trick with the denominators.
You get the same conclusion. United States
It is useful to know that the product of two numbers is equal to the product of their HCF and LCM. So 756 × 1386 = HCF × LCM. Hence we have
Observe that the bracketed number (756/126) is equal to 6 which is the numerator of the reduced fraction. So we do not even need to make that calculation. Just take the reduced numerator 6 and multiply that with the original denominator 1386 to get the LCM. You may try a similar trick with 1386 and 126. You end up multiplying 756 by 11, which gives the same answer.
Try the above with different pairs of numbers. How can you extend this to find the HCF and LCM of three or more numbers?
(*) OK, just kidding. In
, we sort of follow
British English, but we are flexible. Singapore
* Lower Secondary Mathematics (Sec 1 ~ grade 7)
* other syllabuses that involve factors, HCF (GCD) and LCM
* any interested learner