Mathematics
HCF and LCM using prime factorisation
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
Practice questions
Which statement about (84) and (198) is correct?HardLevel 10If the prime factorisations of two numbers are (2^5\times3^2\times5) and (2^3\times3^4\times7), what will be their HCF?HardLevel 11If (72=2^3\times3^2), (120=2^3\times3\times5), and (168=2^3\times3\times7), what is their LCM?HardLevel 11The HCF of two numbers is (24) and their LCM is (720). If one number is (96), what is the other number?HardLevel 11What is the smallest number exactly divisible by (32), (48), and (80)?HardLevel 11What is the greatest number that can exactly divide (144), (216), and (360)?HardLevel 11If the HCF of two numbers is (18) and their LCM is (378), which statement is correct?HardLevel 11If (p=2^4\times3^3\times5) and (q=2^2\times3\times5^2\times11), what is (\frac{\text{LCM}}{\text{HCF}})?HardLevel 11Three bells ring at intervals of (20), (28), and (35) seconds. They ring together now. After how many seconds will they ring together again?HardLevel 11A class has (84) pencils and (126) erasers. They are to be divided into the maximum number of identical packets. How many packets can be made?HardLevel 11What is the smallest number that leaves remainder (5) when divided by (18), (24), and (30)?HardLevel 11If (x=2^a\times3^2\times5) and (y=2^4\times3^b\times7) have HCF (2^3\times3^2), which values are possible?HardLevel 11If (m=2^2\times3^a\times5) and (n=2^5\times3^3\times5^b) have LCM (2^5\times3^4\times5^2), which values can be correct?HardLevel 11The HCF of two numbers is (30) and their LCM is (900). If the numbers are (30a) and (30b), which statement about (a) and (b) is correct?HardLevel 11Which pair has HCF (18) and LCM (540)?HardLevel 11If two numbers are coprime and their LCM is (221), what is their product?HardLevel 11If the HCF of (126) and (315) is (63), what is their LCM?HardLevel 11If (252=2^2\times3^2\times7) and (330=2\times3\times5\times11), how many distinct prime factors will their LCM have?HardLevel 11If a number leaves remainder (3) when divided by (16), (20), and (25), what is the smallest such number?HardLevel 11The prime factorisations of three numbers are (2^2\times3^3), (2^4\times3^2\times5), and (2^3\times3\times7). What is their HCF?HardLevel 11