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
If the HCF of (162), (270), and (378) is found, what will be the power of (3) in it?ExpertLevel 11If the LCM of (112), (180), and (225) is found, how many distinct prime factors will it have?ExpertLevel 11If (L) is the LCM and (H) is the HCF of (2^8\times3^2\times5) and (2^5\times3^6\times5^4), what will be the powers of (5) in (L) and (H) respectively?ExpertLevel 11If the HCF of (169), (221), and (299) is found, what is the correct value?ExpertLevel 11If the HCF of (169), (221), and (299) is asked, which is the correct answer?ExpertLevel 11If the HCF of two numbers is (64) and their LCM is (5120), what will be the total power of (2) in their product?ExpertLevel 11If the HCF of (224) and (336) is (112), what is the difference between their LCM and HCF?ExpertLevel 11If a number is divisible by both (2^6\times3^3\times7) and (2^4\times3^5\times13), what will be the power of (3) in the smallest such number?ExpertLevel 11If two numbers are coprime and their product is (1147), what will be their LCM?ExpertLevel 11The prime factorisations of three numbers are (2^4\times3^2\times5), (2^2\times3^3\times7), and (2^5\times3\times11). What will be their HCF?ExpertLevel 11If the LCM of (68), (85), and (289) is found, what will be the power of (17) in it?ExpertLevel 11The HCF of two numbers is (21) and their LCM is (2310). How many unordered pairs are possible?ExpertLevel 11If the HCF of two numbers is (75) and their LCM is (1950), what is correct about their existence?ExpertLevel 11If the HCF of (132) and (220) is (44), what will be the power of (5) in their LCM?ExpertLevel 11A number is divisible by both (2^5\times3^4\times5) and (2^7\times3^2\times11). What will be the smallest such number?ExpertLevel 11If the HCF of (2^a\times3^3\times5) and (2^6\times3^5\times5^2) is (2^4\times3^3\times5), which value of (a) is possible?ExpertLevel 11If the LCM of (2^4\times3^b\times7) and (2^5\times3^3\times7^2) is (2^5\times3^6\times7^2), what can be the value of (b)?ExpertLevel 11If (a) and (b) are coprime, (a=2^4\times3), and (ab=2496), what is (b)?ExpertLevel 11If (L) is the LCM of (98), (147), and (245), what is the value of (L)?ExpertLevel 11If a number leaves remainder (15) when divided by (40), (56), and (88), what is the smallest such number?ExpertLevel 11